BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Per von Soosten (Harvard University) DTSTART:20200427T201500Z DTEND:20200427T211500Z DTSTAMP:20260422T212558Z UID:Probability/1 DESCRIPTION:Title: Localization and delocalization for ultrametric random matrices\nb y Per von Soosten (Harvard University) as part of MIT probability seminar\ n\n\nAbstract\nWe consider a Dyson-hierarchical analogue of power-law rand om band matrices with Gaussian entries. The model can be constructed recur sively by alternating between averaging independent copies of the matrix a nd running Dyson Brownian motion. We use this to map out the localized reg ime and a large part of the delocalized regime in terms of local statistic s and eigenfunction decay. Our method extends to a part of the delocalized regime in which the model has a well-defined infinite-volume limit with H older-continuous spectral measures. This talk is based on joint work with Simone Warzel.\n LOCATION:https://researchseminars.org/talk/Probability/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Amol Aggarwal (Harvard University) DTSTART:20200504T201500Z DTEND:20200504T211500Z DTSTAMP:20260422T212558Z UID:Probability/2 DESCRIPTION:Title: Pure States in the Ferroelectric Six-Vertex Model\nby Amol Aggarwa l (Harvard University) as part of MIT probability seminar\n\n\nAbstract\nT he classification and analysis of pure states (translation-invariant\, erg odic Gibbs measures) for statistical mechanical systems is a fundamental q uestion in mathematical physics. In this talk we investigate this question for the six-vertex model in its ferroelectric phase. We will see that the situation here differs considerably from its more well-known counterpart for dimer models. In particular\, for the ferroelectric six-vertex model t here now exist non-trivial regions of non-existence and new families of hi ghly anisotropic pure states exhibiting Kardar-Parisi-Zhang (KPZ) fluctuat ions.\n LOCATION:https://researchseminars.org/talk/Probability/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Marianna Russkikh (MIT) DTSTART:20200511T201500Z DTEND:20200511T211500Z DTSTAMP:20260422T212558Z UID:Probability/3 DESCRIPTION:Title: Dimers and embeddings\nby Marianna Russkikh (MIT) as part of MIT p robability seminar\n\n\nAbstract\nOne of the main questions in the context of the universality and conformal invariance of a critical 2D lattice mod el is to find an embedding which geometrically encodes the weights of the model and that admits "nice" discretizations of Laplace and Cauchy-Riemann operators. We establish a correspondence between dimer models on a bipart ite graph and circle patterns with the combinatorics of that graph. We des cribe how to construct a '$t$-embedding' (or a circle pattern) of a dimer planar graph using its Kasteleyn weights\, and develop a relevant theory o f discrete holomorphic functions on $t$-embeddings\; this theory unifies K enyon's holomorphic functions on $T$-graphs and $s$-holomorphic functions coming from the Ising model. We discuss a concept of 'perfect $t$-embeddin gs' of weighted bipartite planar graphs. We believe that these embeddings always exist and that they are good candidates to recover the complex stru cture of big bipartite planar graphs carrying a dimer model. Based on: joi nt work with R. Kenyon\, W. Lam\, S. Ramassamy\; and joint work with D. Ch elkak\, B. Laslier.\n LOCATION:https://researchseminars.org/talk/Probability/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Eitan Bachmat (Ben-Gurion University) DTSTART:20200921T201500Z DTEND:20200921T211500Z DTSTAMP:20260422T212558Z UID:Probability/4 DESCRIPTION:Title: On maximal (weight) increasing subsequences\nby Eitan Bachmat (Ben -Gurion University) as part of MIT probability seminar\n\n\nAbstract\nWe w ill discuss the connection between the first order asymptotics of maximal weight increasing subsequences and comparison of natural (and implemented) airplane boarding policies.\n\nWe then consider the behavior of weight fl uctuations of maximal weight increasing subsequences by viewing them as di screte versions of maximal proper time curves in various space-time domain s.\n LOCATION:https://researchseminars.org/talk/Probability/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Remi Rhodes (Aix-Marseille Université) DTSTART:20200928T201500Z DTEND:20200928T211500Z DTSTAMP:20260422T212558Z UID:Probability/5 DESCRIPTION:Title: Conformal Bootstrap in Liouville theory.\nby Remi Rhodes (Aix-Mars eille Université) as part of MIT probability seminar\n\n\nAbstract\nLiouv ille conformal field theory (denoted LCFT) is a 2-dimensional conformal fi eld theory depending on a real-valued parameter γ and studied since the e ighties in theoretical physics. In the case of the theory on the Riemann s phere\, physicists proposed closed formulae for the n-point correlation fu nctions using symmetries and representation theory\, called the DOZZ formu la (when n=3) and the conformal bootstrap (for n>3). A probabilistic const ruction of LCFT was recently proposed by David-Kupiainen-Rhodes-Vargas for γ in the half-open interval (0\,2] and the last three authors later prov ed the DOZZ formula. In this talk I will present a proof of equivalence be tween the probabilistic and the bootstrap construction (proposed in physic s) for the n point correlation functions with n greater or equal to 4\, va lid for γ in the open interval (0\, √2). Our proof combines the analysi s of a natural semi-group\, tools from scattering theory and the use of Vi rasoro algebra in the context of the probabilistic approach (the so-called conformal Ward identities).\n LOCATION:https://researchseminars.org/talk/Probability/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacapo Borga (Universität Zürich) DTSTART:20201005T201500Z DTEND:20201005T211500Z DTSTAMP:20260422T212558Z UID:Probability/6 DESCRIPTION:Title: Scaling and local limits of Baxter permutations and bipolar orientatio ns through coalescent-walk processes\nby Jacapo Borga (Universität Z ürich) as part of MIT probability seminar\n\n\nAbstract\nBaxter permutati ons\, plane bipolar orientations\, and a specific family of walks in the n on-negative quadrant\, called tandem walks\, are well-known to be related to each other through several bijections. In order to study their scaling and local limits\, we introduce a further new family of discrete objects\, called coalescent-walk processes and we relate them with the other previo usly mentioned families introducing some new bijections.\n\nWe prove joint Benjamini-Schramm convergence (both in the annealed and quenched sense) f or uniform objects in the four families. Furthermore\, we explicitly const ruct a new random measure of the unit square\, called the Baxter permuton\ , and we show that it is the scaling limit (in the permuton sense) of unif orm Baxter permutations. We further relate the limiting objects of the fou r families to each other\, both in the local and scaling limit case.\n\nTo prove the scaling limit result\, we show that the associated random coale scent-walk process converges in distribution to the coalescing flow of a p erturbed version of the Tanaka stochastic differential equation. This resu lt has connections with the results of Gwynne\, Holden\, Sun (2016) on sca ling limits (in the Peanosphere topology) of plane bipolar triangulations. \n\nThis is a joint work with Mickael Maazoun.\n LOCATION:https://researchseminars.org/talk/Probability/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Kolesnikov (HSE) DTSTART:20201026T201500Z DTEND:20201026T211500Z DTSTAMP:20260422T212558Z UID:Probability/8 DESCRIPTION:Title: Blaschke--Santalo inequality for many functions and geodesic barycente rs of measures\nby Alexander Kolesnikov (HSE) as part of MIT probabili ty seminar\n\n\nAbstract\nMotivated by the geodesic barycenter problem fro m optimal transportation theory\, we prove a natural generalization of the Blaschke–Santalo inequality for many sets and many functions. We derive from it an entropy bound for the total Kantorovich cost appearing in the barycenter problem.\n \nThe talk is based on joint works with Elisabeth W erner.\n LOCATION:https://researchseminars.org/talk/Probability/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Damron (Georgia Tech) DTSTART:20201102T211500Z DTEND:20201102T221500Z DTSTAMP:20260422T212558Z UID:Probability/9 DESCRIPTION:Title: Critical first-passage percolation in two dimensions\nby Michael D amron (Georgia Tech) as part of MIT probability seminar\n\n\nAbstract\nIn  2d first-passage percolation (FPP)\, we place nonnegative i.i.d. weights  (te) on the edges of ℤ2 and study the induced weighted graph pseudo metric T=T(x\,y). If we denote by p=ℙ(te=0)\, then there is a transiti on in the large-scale behavior of the model as p varies from 0 to 1. When p<12\, T(0\,x) grows linearly in x\, and when p>12\, it is stoch astically bounded. The critical case\, where p=12\, is more subtle\, and the sublinear growth of T(0\,x) depends on the behavior of the distribut ion function of te near zero. I will discuss my work over the past few y ears that (a) determines the exact rate of growth of T(0\,x)\, (b) determ ines the ``time constant'' for the site-FPP model on the triangular lattic e and\, more recently (c) studies the growth of T(0\,x) in a dynamical v ersion of the model\, where weights are resampled according to independent exponential clocks. These are joint works with J. Hanson\, D. Harper\, W. -K. Lam\, P. Tang\, and X. Wang.\n LOCATION:https://researchseminars.org/talk/Probability/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Atilla Yilmaz (Temple) DTSTART:20201109T211500Z DTEND:20201109T221500Z DTSTAMP:20260422T212558Z UID:Probability/10 DESCRIPTION:Title: Stochastic homogenization of Hamilton-Jacobi equations in one dimensi on\nby Atilla Yilmaz (Temple) as part of MIT probability seminar\n\n\n Abstract\nAfter giving an introduction to the homogenization of Hamilton-J acobi (HJ) equations\, I will focus on HJ equations in one space dimension with Hamiltonians of the form G(p)+βV(x\,ω)\, where V is a stationar y & ergodic potential of unit amplitude. The homogenization of such equati ons is established in a 2016 paper of Armstrong\, Tran and Yu for all cont inuous and coercive G. Under the extra condition that G is a double-wel l function (for the sake of clarity and convenience)\, I will present a ne w and fully constructive proof of homogenization which yields a formula fo r the effective Hamiltonian H‾‾ and clarifies the dependence of H ‾‾ on G\, β and the law of V.\n LOCATION:https://researchseminars.org/talk/Probability/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Subhabrata Sen (Harvard) DTSTART:20201116T211500Z DTEND:20201116T221500Z DTSTAMP:20260422T212558Z UID:Probability/11 DESCRIPTION:Title: Large deviations for dense random graphs: beyond mean-field\nby S ubhabrata Sen (Harvard) as part of MIT probability seminar\n\n\nAbstract\n In a seminal paper\, Chatterjee and Varadhan derived an LDP for the dense Erdős-Rényi random graph\, viewed as a random graphon. This directly pro vides LDPs for continuous functionals such as subgraph counts\, spectral n orms\, etc. In contrast\, very little is understood about this problem if the underlying random graph is inhomogeneous or constrained\n\nIn this tal k\, we will explore large deviations for dense random graphs\, beyond the ``mean-field" setting. In particular\, we will study large deviations for uniform random graphs with given degrees\, and a family of dense block mod el random graphs. We will establish the LDP in each case\, and identify th e rate function. In the block model setting\, we will use this LDP to stud y the upper tail problem for homomorphism densities of regular sub-graphs. Our results establish that this problem exhibits a symmetry/symmetry-brea king transition\, similar to one observed for Erdős-Rényi random graphs. \n\nBased on joint works with Christian Borgs\, Jennifer Chayes\, Souvik D hara\, Julia Gaudio and Samantha Petti.\n LOCATION:https://researchseminars.org/talk/Probability/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Benson Au (UCSD) DTSTART:20201207T211500Z DTEND:20201207T221500Z DTSTAMP:20260422T212558Z UID:Probability/13 DESCRIPTION:Title: Finite-rank perturbations of random band matrices via infinitesimal f ree probability\nby Benson Au (UCSD) as part of MIT probability semina r\n\n\nAbstract\nFree probability provides a unifying framework for studyi ng random multi-matrix models in the large N limit. Typically\, the purvie w of these techniques is limited to invariant or mean-field ensembles.\n N evertheless\, we show that random band matrices fit quite naturally in thi s framework. Our considerations extend to the infinitesimal level\, where finer results can be stated for the 1/N correction. Our results allow us t o extend previous work of Shlyakhtenko\n on finite-rank perturbations of W igner matrices in the infinitesimal framework. For finite-rank perturbatio ns of our model\, we find outliers at the classical positions from the def ormed Wigner ensemble.\n LOCATION:https://researchseminars.org/talk/Probability/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Russell Lyons (Indiana University) DTSTART:20200914T201500Z DTEND:20200914T211500Z DTSTAMP:20260422T212558Z UID:Probability/15 DESCRIPTION:Title: Random Walks on Dyadic Lattice Graphs and Their Duals\nby Russell Lyons (Indiana University) as part of MIT probability seminar\n\n\nAbstra ct\nDyadic lattice graphs and their duals are commonly used as discrete ap proximations to the hyperbolic plane. We use them to give examples of rand om rooted graphs that are stationary for simple random walk\, but whose du als have only a singular stationary measure. This answers a question of Cu rien and shows behaviour different from the unimodular case. The consequen ce is that planar duality does not combine well with stationary random gra phs. We also study harmonic measure on dyadic lattice graphs and show its singularity. Much interesting behaviour observed numerically remains to be explained. No background will be assumed for the talk. This is joint work with Graham White.\n\nDate: Monday\, September 14. \nTime: There will be an informal discussion for MIT local people with our speaker starting at 4 pm and the talk starts at the usual time 4:15 pm. Welcome to join the dis cussion before the talk and to say hi to the speaker and other attendees.\ n\nZoom: https://mit.zoom.us/j/96421029678?pwd=cThIR2hVNUNpY1JDOS95RUpoeFp mdz09​\n\nPassword: 356815\n\nPlease download and import the following i Calendar (.ics) files to your calendar system.\nhttps://mit.zoom.us/meetin g/tJIpdeiorDIsHdxRBXOnKJeRp0PlkQLDSHeo/ics?icsToken=98tyKuCuqjkrGtacth6PRo wABojod_TzplhdgqdFrj3dLC54SAbEJrJyPrlOPPzj\n\n\nYou can check out more det ails about the seminar at https://math.mit.edu/seminars/probability/\n\nHo pe you see you on Monday\,\nYilin\n LOCATION:https://researchseminars.org/talk/Probability/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Christophe Mourrat (New York University) DTSTART:20201019T201500Z DTEND:20201019T211500Z DTSTAMP:20260422T212558Z UID:Probability/16 DESCRIPTION:Title: Mean-field spin glasses: beyond the replica trick?\nby Jean-Chris tophe Mourrat (New York University) as part of MIT probability seminar\n\n \nAbstract\nSpin glasses are models of statistical mechanics encoding diso rdered interactions between many simple units. One of the fundamental quan tities of interest is the free energy of the model\, in the limit when the number of units tends to infinity. For a restricted class of models\, thi s limit was predicted by Parisi\, and later rigorously proved by Guerra an d Talagrand. I will first show how to rephrase this result using an infini te-dimensional Hamilton-Jacobi equation. I will then present partial resul ts suggesting that this new point of view may allow to understand limit fr ee energies for a larger class of models\, focusing in particular on the c ase in which the units are organized over two layers\, and only interact a cross layers.\n LOCATION:https://researchseminars.org/talk/Probability/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Mikulincer (Weizmann Institute) DTSTART:20201130T191500Z DTEND:20201130T201500Z DTSTAMP:20260422T212558Z UID:Probability/17 DESCRIPTION:Title: Functional inequalities in Gauss space\nby Dan Mikulincer (Weizma nn Institute) as part of MIT probability seminar\n\n\nAbstract\nWe will di scuss how several known functional inequalities\, such as log-Sobolev and Shannon-Stam\, arise from general principles in stochastic analysis. This point of view will give rise to a unified framework from which one may stu dy the stability of those inequalities. Several results in this direction will be presented with further applications to central limit theorems\, no rmal approximations and optimal transport.\n\nOur method is based on an en tropy-minimizing process from stochastic control theory\, which allows us to express entropy as a solution to a variational problem.\n\nBased on joi nt works with Ronen Eldan\, Alex Zhai and Yair Shenfeld\n LOCATION:https://researchseminars.org/talk/Probability/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Hariharan Narayanan (TIFR\, Mumbai) DTSTART:20210222T161500Z DTEND:20210222T171500Z DTSTAMP:20260422T212558Z UID:Probability/18 DESCRIPTION:Title: Random discrete concave functions on an equilateral lattice with peri odic boundary conditions\nby Hariharan Narayanan (TIFR\, Mumbai) as pa rt of MIT probability seminar\n\n\nAbstract\nMotivated by connections to r andom matrices\, Littlewood-Richardson coefficients and square-triangle ti lings\, we study random discrete concave functions on an equilateral latti ce\, where the Hessian satisfies periodic boundary conditions and has a gi ven average s. Defining surface tension sigma to be the negative of a cert ain limiting differential entropy per site\, we show that sigma is a well defined convex function of s. When s is such that sigma is strictly convex \, we show that the corresponding rescaled random surfaces concentrate in the sup norm as the length scale of the periodicity n tends to infinity. W e also show that concentration occurs when the gradient of sigma belongs t o a certain cone\, and in this case obtain quantitative bounds for the con centration.\n\nA preprint can be found at https://arxiv.org/abs/2005.1337 6 .\n LOCATION:https://researchseminars.org/talk/Probability/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Alberts (University of Utah) DTSTART:20210301T211500Z DTEND:20210301T221500Z DTSTAMP:20260422T212558Z UID:Probability/19 DESCRIPTION:Title: Loewner Dynamics for the Multiple SLE(0) Process\nby Tom Alberts (University of Utah) as part of MIT probability seminar\n\n\nAbstract\nRec ently Peltola and Wang introduced the multiple SLE(0) process as the deter ministic limit of the random multiple SLE(κ) curves as κ goes to zero. T hey prove this result by means of a ``small κ" large deviations principle \, but the limiting curves also turn out to have important geometric chara cterizations that are independent of their relation to SLE(κ). In particu lar\, they show that the SLE(0) curves can be generated by a deterministic Loewner evolution driven by multiple points\, and the vector field descri bing the evolution of these points must satisfy a particular system of alg ebraic equations. We show how to generate solutions to these algebraic equ ations in two ways: first in terms of the poles and critical points of an associated real rational function\, and second via the well-known Calogero -Moser integrable system with particular initial velocities. Although our results are purely deterministic they are again motivated by taking limits of probabilistic constructions\, which I will explain.\n LOCATION:https://researchseminars.org/talk/Probability/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin McKenna (NYU) DTSTART:20210315T201500Z DTEND:20210315T211500Z DTSTAMP:20260422T212558Z UID:Probability/20 DESCRIPTION:Title: Random determinants and landscape complexity beyond invariance\nb y Benjamin McKenna (NYU) as part of MIT probability seminar\n\n\nAbstract\ nThe Kac-Rice formula allows one to study the complexity of high-dimension al Gaussian random functions (meaning asymptotic counts of critical points ) via the determinants of large random matrices. We present a new result o n determinant asymptotics for non-invariant random matrices\, and use it t o compute (annealed) complexity for several types of landscapes. These inc lude (i) the elastic manifold\, where we identify the "Larkin mass" separa ting order and disorder\, verifying results of Fyodorov-Le Doussal\, and ( ii) soft spins in an anisotropic well\, where we find a new phase transiti on with universal quadratic and cubic near-critical behavior. This extends the pioneering complexity results of Fyodorov and Auffinger-Ben Arous-Cer ny. Joint work with Gerard Ben Arous and Paul Bourgade.\n LOCATION:https://researchseminars.org/talk/Probability/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Shirshendu Ganguly (UC Berkeley) DTSTART:20210322T201500Z DTEND:20210322T211500Z DTSTAMP:20260422T212558Z UID:Probability/21 DESCRIPTION:Title: Stability and chaos in dynamical last passage percolation\nby Shi rshendu Ganguly (UC Berkeley) as part of MIT probability seminar\n\n\nAbst ract\nMany complex disordered systems in statistical mechanics are charact erized by intricate energy landscapes. The ground state\, the configuratio n with the lowest energy\, lies at the base of the deepest valley. In impo rtant examples\, such as Gaussian polymers and spin glass models\, the lan dscape has many valleys and the abundance of near-ground states (at the ba se of the valleys) indicates the phenomenon of chaos\, under which the gro und state alters profoundly when the disorder of the model is slightly per turbed.\n\nIn this talk\, we will discuss a recent work with Alan Hammond computing the critical exponent that governs the onset of chaos in a dynam ic manifestation of a canonical planar last passage percolation model in t he Kardar-Parisi-Zhang universality class. We expect this exponent to be u niversal across a wide range of interface and stochastic growth models. Th e arguments rely on Chatterjee's harmonic analytic theory of equivalence o f super-concentration and chaos in Gaussian spaces and a refined understan ding of the corresponding static landscape geometry.\n LOCATION:https://researchseminars.org/talk/Probability/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio (Tuca) Auffinger (Northwestern) DTSTART:20210329T140000Z DTEND:20210329T150000Z DTSTAMP:20260422T212558Z UID:Probability/22 DESCRIPTION:Title: TAP equations and ground states of generalized spin glass models\ nby Antonio (Tuca) Auffinger (Northwestern) as part of MIT probability sem inar\n\n\nAbstract\nIn this talk\, I will survey models of spin glasses wh ere the spins take values either in a ball in $\\mathbb R^d$ or in a large subset of the integers. I will discuss two important quantities: the TAP equations\, a system of self-consistent equations relating the spin magnet ization at high temperature\, and the ground-state energy\, the minimum of the Hamiltonian. During the talk\, I will stress the differences and the new difficulties that appear when one compares these models to classical m odels such as the Sherrington-Kirkpatrick or the spherical p-spin model. B ased on joint works with Cathy Chen (Northwestern) and Yuxin Zhou (Northwe stern).\n\nSeminar Zoom link: https://mit.zoom.us/j/96421029678?pwd=cThIR2 hVNUNpY1JDOS95RUpoeFpmdz09​ \n\nPassword: 356815​\n\nSeminar webpage: https://math.mit.edu/probability/\n\nSeminar Zoom link: https://mit.zoom. us/j/96421029678?pwd=cThIR2hVNUNpY1JDOS95RUpoeFpmdz09​ \n\nPassword: 35 6815​\n\nSeminar webpage: https://math.mit.edu/probability/\n LOCATION:https://researchseminars.org/talk/Probability/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Masha Gordina (UConn) DTSTART:20210405T201500Z DTEND:20210405T211500Z DTSTAMP:20260422T212558Z UID:Probability/23 DESCRIPTION:Title: Uniform volume doubling and functional inequalities on Lie groups \nby Masha Gordina (UConn) as part of MIT probability seminar\n\n\nAbstrac t\nOn a compact Lie group with a left-invariant Riemannian metric\, many i mportant functional inequalities for the Laplacian (such as Poincar\\'e in equality\, parabolic Harnack inequality\, etc.)  can be proved using only the volume doubling property.  That is\,  constants in these inequaliti es can be controlled by the doubling constant of the metric\; this can be strictly more powerful than classical techniques involving Ricci curvature lower bounds.  It can happen that there is a uniform bound on the doubli ng constants of all left-invariant metrics on a given Lie group\; such a g roup is called uniformly doubling.  In such a case\, the implicit constan ts in the functional inequalities will also be uniformly bounded over all left-invariant metrics.  We show that this happens for the special unitar y group SU(2)\, via explicit uniform volume estimates and describe the con sequences (heat kernel estimates\, Weyl counting function etc)\n\nThis is joint work with Nate Eldredge and Laurent Saloff-Coste.\n LOCATION:https://researchseminars.org/talk/Probability/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan Dauvergne (Princeton) DTSTART:20210412T201500Z DTEND:20210412T211500Z DTSTAMP:20260422T212558Z UID:Probability/24 DESCRIPTION:Title: The directed landscape.\nby Duncan Dauvergne (Princeton) as part of MIT probability seminar\n\n\nAbstract\nThe directed landscape is a rand om `directed metric' on the spacetime plane that arises as the scaling lim it of integrable models of last passage percolation. It is expected to be the universal scaling limit for all models in the KPZ universality class f or random growth. In this talk\, I will describe its construction in terms of the Airy line ensemble\, give an extension of this construction for op timal length disjoint paths\, and discuss probabilistic consequences of th ese constructions. Based on joint work with J. Ortmann\, B. Virag\, and L. Zhang.\n LOCATION:https://researchseminars.org/talk/Probability/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Shriver (UCLA) DTSTART:20210426T201500Z DTEND:20210426T211500Z DTSTAMP:20260422T212558Z UID:Probability/25 DESCRIPTION:Title: Free energy\, Gibbs measures\, and Glauber dynamics on trees\nby Christopher Shriver (UCLA) as part of MIT probability seminar\n\n\nAbstrac t\nI will introduce some ideas from sofic entropy theory and use them to d efine a notion of free energy density in the context of finite-alphabet\, nearest-neighbor interactions (like the Ising model) indexed by infinite r egular trees. This free energy is used to prove that shift-invariant measu res are Gibbs if and only if they are Glauber-invariant. We also establish a metastability phenomenon for the corresponding dynamics on finite local ly-tree-like regular graphs. These results can be combined to characterize maximal-entropy joinings of Gibbs measures.\n LOCATION:https://researchseminars.org/talk/Probability/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Youngtak Sohn (Stanford) DTSTART:20210503T201500Z DTEND:20210503T211500Z DTSTAMP:20260422T212558Z UID:Probability/26 DESCRIPTION:Title: Replica symmetry breaking for random regular NAE-SAT\nby Youngtak Sohn (Stanford) as part of MIT probability seminar\n\n\nAbstract\nIn a wi de class of random constraint satisfaction problems\, ideas from statistic al physics predict that there is a rich set of phase transitions governed by one-step replica symmetry breaking(1RSB). In particular\, it is conject ured that there is the condensation regime below the satisfiability thresh old\, where the solution space condenses into the large clusters. We estab lish this phenomenon for the random regular NAE-SAT model by showing that most of the solutions lie in a bounded number of clusters and the overlap of two independent solutions concentrates on two points. Central to the pr oof is to calculate the moments of the number of clusters whose size is in an O(1) window.\n LOCATION:https://researchseminars.org/talk/Probability/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Morris (Jie Jun) Ang (MIT) DTSTART:20210510T201500Z DTEND:20210510T211500Z DTSTAMP:20260422T212558Z UID:Probability/27 DESCRIPTION:Title: Integrability of the conformal loop ensemble\nby Morris (Jie Jun) Ang (MIT) as part of MIT probability seminar\n\n\nAbstract\nFor $\\frac{8 }{3} < \\kappa < 8$\, the conformal loop ensemble $\\mathrm{CLE}_{\\kappa} $ is a canonical random ensemble of loops which is conformally invariant i n law\, and whose loops locally look like Schramm-Loewner evolution with p arameter $\\kappa$. It describes the scaling limits of the Ising model\, p ercolation\, and other models. When $\\kappa \\leq 4$ the loops are simple curves. In this regime\, we compute the three-point function of $\\mathrm {CLE}_{\\kappa}$ on the sphere and show it agrees with the imaginary DOZZ formula of Zamolodchikov (2005). We also verify a conjecture of Kenyon and Wilson on the electrical thickness of $\\mathrm{CLE}_{\\kappa}$ on the sp here. Our arguments depend on couplings of $\\mathrm{CLE}$ with Liouville quantum gravity and the integrability of Liouville conformal field theory. \nBased on joint work with Xin Sun\, which builds on our recent work with Holden and Remy.\n LOCATION:https://researchseminars.org/talk/Probability/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Minjae Park (MIT) DTSTART:20210517T201500Z DTEND:20210517T211500Z DTSTAMP:20260422T212558Z UID:Probability/28 DESCRIPTION:Title: Wilson loop expectations as sums over surfaces in 2D\nby Minjae P ark (MIT) as part of MIT probability seminar\n\n\nAbstract\nAlthough latti ce Yang-Mills theory on $\\mathbb Z^d$ is easy to rigorously define\, the construction of a satisfactory continuum theory on $\\mathbb R^d$ is a maj or open problem when $d \\geq 3$. Such a theory should assign a Wilson loo p expectation to each collection of loops in $\\mathbb R^d$. One of the pr oposed approaches involves representing this quantity as a sum over surfac es having the loops as their boundary. There are some formal/heuristic way s to make sense of this notion\, but they typically yield an ill-defined d ifference of infinities. The goal of this talk is to make sense of Yang-Mi lls integrals as surface sums in the special case that $d=2$\, where the e xistence of a well-defined continuum theory is already well known. We also obtain an alternative proof of the Makeenko-Migdal equation\, and Levy's formula based on the Schur-Weyl duality.\n\nJoint work with Joshua Pfeffer \, Scott Sheffield\, and Pu Yu.\n LOCATION:https://researchseminars.org/talk/Probability/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Jimmy He (MIT) DTSTART:20210913T201500Z DTEND:20210913T211500Z DTSTAMP:20260422T212558Z UID:Probability/29 DESCRIPTION:Title: Random walks on finite fields with deterministic jumps\nby Jimmy He (MIT) as part of MIT probability seminar\n\nLecture held in Room: 2-147 in the Simons Building.\n\nAbstract\nRecently\, Chatterjee and Diaconis s howed that most bijections\, if applied between steps of a Markov chain\, cause the resulting chain to mix much faster. However\, explicit examples of this speedup phenomenon are rare. I will discuss recent work studying s uch walks on finite fields where the bijection is algebraically defined. T his work gives a large collection of examples where this speedup phenomeno n occurs. These walks can be seen as a non-linear analogue of the Chung-Di aconis-Graham process\, where the bijection is multiplication by a non-zer o element of the finite field. This work is partially joint with Huy Pham and Max Xu.\n LOCATION:https://researchseminars.org/talk/Probability/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Yves Gaudreau Lamarre (University of Chicago) DTSTART:20210920T201500Z DTEND:20210920T211500Z DTSTAMP:20260422T212558Z UID:Probability/30 DESCRIPTION:Title: Number rigidity in the spectrum of random Schrödinger operators\ nby Pierre Yves Gaudreau Lamarre (University of Chicago) as part of MIT pr obability seminar\n\n\nAbstract\nIn this talk\, I will discuss recent prog ress in the understanding of the structure in the spectrum of random Schr ödinger operators. More specifically\, I will introduce the concept of nu mber rigidity in point processes and discuss recent efforts to understand its occurrence in the spectrum of random Schrödinger operators. Based on joint works with Promit Ghosal (MIT)\, Wenxuan Li (UChicago)\, and Yuchen Liao (Warwick).\n LOCATION:https://researchseminars.org/talk/Probability/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Lisa Sauermann (MIT) DTSTART:20210927T201500Z DTEND:20210927T211500Z DTSTAMP:20260422T212558Z UID:Probability/31 DESCRIPTION:Title: On the extension complexity of random polytopes.\nby Lisa Sauerma nn (MIT) as part of MIT probability seminar\n\nLecture held in Room: 2 - 1 47 in the Simons Building.\n\nAbstract\nSometimes\, it is possible to repr esent a complicated polytope as a projection of a much simpler polytope. T o quantify this phenomenon\, the extension complexity of a polytope P is d efined to be the minimum number of facets in a (possibly higher-dimensiona l) polytope from which P can be obtained as a (linear) projection. In this talk\, we discuss some results on the extension complexity of random poly topes. For a fixed dimension d\, we consider random d-dimensional polytope s obtained as the convex hull of independent random points either in the u nit ball ball or on the unit sphere. In both cases\, we prove that the ext ension complexity is typically on the order of the square root of number o f vertices of the polytope. Joint work with Matthew Kwan and Yufei Zhao.\n LOCATION:https://researchseminars.org/talk/Probability/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Cook (Duke) DTSTART:20211004T201500Z DTEND:20211004T211500Z DTSTAMP:20260422T212558Z UID:Probability/32 DESCRIPTION:Title: Large deviations and regularity method for sparse random hypergraphs< /a>\nby Nick Cook (Duke) as part of MIT probability seminar\n\n\nAbstract\ nThe "infamous upper tail" problem for subgraph counts in Erdős–Rényi graphs has received considerable attention since it was popularized by Jan son and Rucinski\, and has connections with questions in graph limit theor y and statistical physics. I will survey work in this area and discuss a n ew approach for the more general setting of hypergraphs\, based on an exte nsion of the regularity method to sparse hypergraphs. In particular\, we d evelop a sparse counting lemma and decomposition theorem for tensors under a novel class of norms that generalize the matrix cut norm. Based on join t work with Amir Dembo and Huy Tuan Pham.\n LOCATION:https://researchseminars.org/talk/Probability/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Matan Harel (Northeastern University) DTSTART:20211018T201500Z DTEND:20211018T211500Z DTSTAMP:20260422T212558Z UID:Probability/33 DESCRIPTION:Title: Quantitative estimates on the effect of random disorder on low-dimens ional lattice models\nby Matan Harel (Northeastern University) as part of MIT probability seminar\n\nLecture held in MIT Room 2-147.\n\nAbstract \nIn their seminal work\, Imry and Ma predicted that the addition of an ar bitrarily small random external field to a low-dimensional statistical phy sics model causes the usual first-order phase transition to be `rounded-of f.' This phenomenon was proven rigorously by Aizenman and Wehr in 1989 for a vastly general class of spin systems and random perturbations. Recently \, the effect was quantified for the random-field Ising model\, proving th at it exhibits exponential decay of correlations at all temperatures. Unfo rtunately\, the analysis relies on the monotonicity (FKG) properties which are not present in many other classical models of interest. This talk wil l present quantitative versions of the Aizenman-Wehr theorems for general spin systems with random disorder\, including Potts\, spin O(n)\, spin gla sses\, and random surface models. This is joint work with Paul Dario and R on Peled.\n LOCATION:https://researchseminars.org/talk/Probability/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Bates (Wisconsin) DTSTART:20211025T201500Z DTEND:20211025T211500Z DTSTAMP:20260422T212558Z UID:Probability/34 DESCRIPTION:Title: Empirical measures\, geodesic lengths\, and a variational formula in first-passage percolation.\nby Erik Bates (Wisconsin) as part of MIT p robability seminar\n\n\nAbstract\nWe consider the standard first-passage p ercolation model on Z^d\, in which each edge is assigned an i.i.d. nonnega tive weight\, and the passage time between any two points is the smallest total weight of a nearest-neighbor path between them. Our primary interest is in the empirical measures of edge-weights observed along geodesics fro m 0 to [n\\xi]\, where \\xi is a fixed unit vector. For various dense fami lies of edge-weight distributions\, we prove that these measures converge weakly to a deterministic limit as n tends to infinity. The key tool is a new variational formula for the time constant. In this talk\, I will deriv e this formula and discuss its implications for the convergence of both em pirical measures and lengths of geodesics.\n LOCATION:https://researchseminars.org/talk/Probability/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Dunlap (NYU Courant) DTSTART:20211108T211500Z DTEND:20211108T221500Z DTSTAMP:20260422T212558Z UID:Probability/35 DESCRIPTION:Title: Fluctuations of solutions to the KPZ equation on a large torus\nb y Alex Dunlap (NYU Courant) as part of MIT probability seminar\n\nLecture held in Seminar in Simon's Building room: 2-147.\n\nAbstract\nI will discu ss proofs of optimal (up to constants) variance bounds on the solutions to the KPZ equation on a torus\, as the time scale and the size of the torus are taken to infinity together\, in the super-relaxation regime and part of the relaxation regime. The arguments are based on stochastic analysis a nd do not use a connection to a discrete system. Joint work with Yu Gu and Tomasz Komorowski.\n LOCATION:https://researchseminars.org/talk/Probability/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Han Huang (Georgia Tech) DTSTART:20211115T211500Z DTEND:20211115T221500Z DTSTAMP:20260422T212558Z UID:Probability/36 DESCRIPTION:Title: Title to be announced\nby Han Huang (Georgia Tech) as part of MIT probability seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Probability/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Ellen Powell (Durham) DTSTART:20211122T211500Z DTEND:20211122T221500Z DTSTAMP:20260422T212558Z UID:Probability/37 DESCRIPTION:Title: Brownian excursions\, conformal loop ensembles and critical Liouville quantum gravity\nby Ellen Powell (Durham) as part of MIT probability seminar\n\n\nAbstract\nIn a groundbreaking work\, Duplantier\, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by the mating of tw o continuum random trees. In this talk I will discuss the counterpart of t heir result for critical LQG and SLE. More precisely\, I will explain how\ , as we approach criticality from the subcritical regime\, the space-filli ng SLE degenerates to the uniform CLE_4 exploration introduced by Werner a nd Wu\, together with a collection of independent coin tosses indexed by t he branch points of the exploration. Furthermore\, although the pair of co ntinuum random trees collapse to a single continuum random tree in the lim it we can apply an appropriate affine transform to the encoding Brownian m otions before taking the limit\, and get convergence to a Brownian half-pl ane excursion. I will try to explain how observables of interest in the cr itical CLE decorated LQG picture are encoded by a growth fragmentation nat urally embedded in the Brownian excursion. This talk is based on joint wor k with Juhan Aru\, Nina Holden and Xin Sun.\n LOCATION:https://researchseminars.org/talk/Probability/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Lingfu Zhang (Princeton) DTSTART:20211129T211500Z DTEND:20211129T221500Z DTSTAMP:20260422T212558Z UID:Probability/38 DESCRIPTION:Title: The environment seen from a geodesic in last-passage percolation. \nby Lingfu Zhang (Princeton) as part of MIT probability seminar\n\n\nAbst ract\nIn exponential directed last-passage percolation\, each vertex in $Z ^2$ is assigned an i.i.d. exponential weight\, and the geodesic between a pair of vertices refers to the up-right path connecting them\, with the ma ximum total weight along the path. It is a natural question to ask what a geodesic looks like locally\, and how weights on and nearby the geodesic b ehave. In this talk\, I will present some new results on this. We show con vergence of the distribution of the ‘environment’ as seen from a typic al point along the geodesic\, and convergence of the corresponding empiric al measure\, as the geodesic length goes to infinity. In addition\, we obt ain an explicit description of the limiting environment\, which depends on the direction of the geodesic. This in principle enables one to compute a ll the local statistics of the geodesic\, and I will talk about some surpr ising and interesting examples. This is based on joint work with James Mar tin and Allan Sly.\n LOCATION:https://researchseminars.org/talk/Probability/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Yury Polyansky (MIT) DTSTART:20211206T211500Z DTEND:20211206T221500Z DTSTAMP:20260422T212558Z UID:Probability/39 DESCRIPTION:Title: Uniqueness of BP fixed point for Ising models.\nby Yury Polyansky (MIT) as part of MIT probability seminar\n\n\nAbstract\nIn the study of I sing models on large locally tree-like graphs\, in both rigorous and non-r igorous methods one is often led to understanding the so-called belief pro pagation distributional recursions and its fixed point (also known as Beth e fixed point\, cavity equation etc). In this work we prove there is at mo st one non-trivial fixed point for Ising models with zero or random (but ` `unbiased'') external fields.\n
\n
\n As a concrete example\, consider a sample A of Ising model on a rooted tree (re gular\, Galton-Watson\, etc). Let B be a noisy version of A obtained by in dependently perturbing each spin as follows: $B_v$ equals to $A_v$ with so me small probability $\\delta$ and otherwise taken to be a uniform +-1 (al ternatively\, 0). We show that the distribution of the root spin $A_\\rh o$ conditioned on values $B_v$ of all vertices $v$ at a large distance fro m the root is independent of $\\delta$ and coincides with $\\delta=0$. Pr eviously this was only known for sufficiently ``low-temperature'' models. Our proof consists of constructing a metric under which the BP operator is a contraction (albeit non-multiplicative). I hope to convince you our pro of is technically rather simple.\n
\n
\n Th is simultaneously closes the following 5 conjectures in the literature:\n
\n \n
  • uselessness of global informatio n for a labeled 2-community stochastic block model\, or 2-SBM (Kanade-Moss el-Schramm'2014)\;
    • \n
  • optimality of local algorithms for 2-SBM under noisy side information (Mossel-Xu'201 5)\;
    • \n
  • independence of robust r econstruction accuracy to leaf noise in broadcasting on trees (Mossel-Neem an-Sly'2016)\;
    • \n
  • boundary irrel evance in BOT (Abbe-Cornacchia-Gu-P.'2021)\;
    • \n
  • characterization of entropy of community labels given the graph in 2-SBM (ibid).
    • \n \n
    \n
    \n Joint work with Qian Yu (Princeton).

    \n LOCATION:https://researchseminars.org/talk/Probability/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Hilario (UFMG) DTSTART:20211101T201500Z DTEND:20211101T211500Z DTSTAMP:20260422T212558Z UID:Probability/40 DESCRIPTION:Title: Random walks on dynamic random environments with non-uniform mixing.< /a>\nby Marcelo Hilario (UFMG) as part of MIT probability seminar\n\n\nAbs tract\nIn this talk\, we will discuss recent results on the limiting behav ior of random walks in dynamic random environments. We will mainly discuss the case when the random walk evolves on one-dimensional random environme nts given by conservative interacting particle systems such as the simple symmetric exclusion process. Its transitions probabilities will depend on the current occupation environment nearby. Conservation of particles leads to poor mixing conditions and we explain how renormalization techniques c an be useful to obtain the law of large numbers\, large deviation estimate s\, and sometimes central limit theorems. The talk is based on several joi nt works with Oriane Blondel\, Frank den Hollander\, Daniel Kious\, Renato dos Santos\, Vladas Sidoravicius and Augusto Teixeira.\n LOCATION:https://researchseminars.org/talk/Probability/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Nishant Changotia (Tata Institute of Fundamental Research) DTSTART:20211213T211500Z DTEND:20211213T221500Z DTSTAMP:20260422T212558Z UID:Probability/41 DESCRIPTION:Title: Title to be announced\nby Nishant Changotia (Tata Institute of Fu ndamental Research) as part of MIT probability seminar\n\n\nAbstract\nAbst ract to be shared\n LOCATION:https://researchseminars.org/talk/Probability/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Cole Graham (Brown University) DTSTART:20220214T211500Z DTEND:20220214T221500Z DTSTAMP:20260422T212558Z UID:Probability/42 DESCRIPTION:Title: Stationary measures for stochastic conservation laws\nby Cole Gra ham (Brown University) as part of MIT probability seminar\n\n\nAbstract\n\ \noindent At long times\, many SPDEs relax to statistically steady states. In this talk\, I will consider the existence and uniqueness of such stati onary measures for stochastically-forced viscous conservation laws on the line. A special case\, the stochastic Burgers equation\, has received a gr eat deal of attention due to its links to the KPZ and stochastic heat equa tions. Stochastic Burgers is known to admit a unique spacetime-stationary ergodic measure for each mean. However\, existing proofs rely on the Cole –Hopf transformation\, which does not extend to other conservation laws. I will discuss a comparison-based approach that recovers partial results for more general conservation laws. In particular\, such SPDEs admit infin itely many stationary ergodic measures\, and there is at most one such mea sure for each mean. \\\\\n\\vspace{2ex}\n\\noindent This is joint work wit h Theodore Drivas\, Alexander Dunlap\, Joonhyun La\, and Lenya Ryzhik.\n LOCATION:https://researchseminars.org/talk/Probability/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Sellke (Stanford University) DTSTART:20220307T211500Z DTEND:20220307T221500Z DTSTAMP:20260422T212558Z UID:Probability/43 DESCRIPTION:Title: Algorithmic Thresholds in Mean-Field Spin Glasses\nby Mark Sellke (Stanford University) as part of MIT probability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract\n\\noindent I will expla in recent progress on computing approximate ground states of mean-field sp in glass Hamiltonians\, which are certain random functions in high dimensi on. While the asymptotic ground state energy OPT is given by the famous Pa risi formula\, the landscape of these functions often include many bad loc al optima which impede optimization by efficient algorithms. In the positi ve direction\, I will explain algorithms based on approximate message pass ing which asymptotically achieve a value ALG given by an extended Parisi f ormula. The case ALG=OPT has a "no overlap gap" or "full replica symmetry breaking" interpretation\, but in general these algorithms may fail to rea ch asymptotic optimality. In the negative direction\, I will explain why n o algorithm with suitably Lipschitz dependence on the random disorder can surpass the threshold ALG. This result applies to many standard optimizati on algorithms\, such as gradient descent and its variants on dimension-fre e time scales. Based on joint works with Ahmed El Alaoui\, Brice Huang\, a nd Andrea Montanari.\n LOCATION:https://researchseminars.org/talk/Probability/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Oanh Nguyen (Brown University) DTSTART:20220328T201500Z DTEND:20220328T211500Z DTSTAMP:20260422T212558Z UID:Probability/44 DESCRIPTION:Title: Survival time of the contact process on random graphs\nby Oanh Ng uyen (Brown University) as part of MIT probability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract\n\\noindent The contact process is a model for the spread of infections on graphs. In this talk\, we discuss the contact process on random graphs with low infection rate $ \\lambda$. For random $d$-regular graphs\, it is known that the survival t ime is $O(\\log n)$ below the critical $\\lambda_c$. By contrast\, on the Erdos-Renyi random graphs $G(n\,d/n)$\, rare high degree vertices result in much longer survival times. We show that the survival time is governed by high density local configurations\, in particular large connected compo nents of high degree vertices on which the infection lasts for time $n^{\\ lambda^{2+o(1)}}$. We shall discuss how to obtain a matching upper bound. Our methods\, moreover\, generalize to random graphs with given degree di stributions that have exponential moments.\\\\\n\\vspace{2ex}\n\\noindent Joint work with Allan Sly. \\\\\n LOCATION:https://researchseminars.org/talk/Probability/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Alt (Courant Institute) DTSTART:20220404T201500Z DTEND:20220404T211500Z DTSTAMP:20260422T212558Z UID:Probability/45 DESCRIPTION:Title: Localization and Delocalization in Erdős–Rényi graphs\nby Joh annes Alt (Courant Institute) as part of MIT probability seminar\n\nLectur e held in Room 2-147 in the Simons Building.\n\nAbstract\nWe consider the Erdős–Rényi graph on N vertices with edge probability d/N. It is well known that the structure of this graph changes drastically when d is of or der log N. Below this threshold it develops inhomogeneities which lead to the emergence of localized eigenvectors\, while the majority of the eigenv ectors remains delocalized. In this talk\, I will present the phase diagra m depicting these localized and delocalized phases and our recent progress in establishing it rigorously.\n\nThis is based on joint works with Rapha el Ducatez and Antti Knowles.\n LOCATION:https://researchseminars.org/talk/Probability/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sky Cao (Stanford University) DTSTART:20220411T201500Z DTEND:20220411T211500Z DTSTAMP:20260422T212558Z UID:Probability/46 DESCRIPTION:Title: Exponential decay of correlations in finite gauge group lattice gauge theories\nby Sky Cao (Stanford University) as part of MIT probability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract \nLattice gauge theories with finite gauge groups are statistical mechanic al models\, very much akin to the Ising model\, but with some twists. In t his talk\, I will describe how to show exponential decay of correlations f or these models at low temperatures. This is based on joint work with Arka Adhikari.\n LOCATION:https://researchseminars.org/talk/Probability/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Ahn (Cornell University) DTSTART:20220425T201500Z DTEND:20220425T211500Z DTSTAMP:20260422T212558Z UID:Probability/47 DESCRIPTION:Title: Lyapunov Exponents of Random Matrix Products and Brownian Motion on G L(n\,C)\nby Andrew Ahn (Cornell University) as part of MIT probability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract \nConsider the discrete-time process formed by the singular values of prod ucts of random matrices\, where time corresponds to the number of matrix f actors. It is known due to Oseledets' theorem that under general assumptio ns\, the Lyapunov exponents converge as the number of matrix factors tend to infinity. In this talk\, we consider random matrices with distributiona l invariance under right multiplication by unitary matrices\, which includ e Ginibre matrices and truncated unitary matrices. The corresponding singu lar value process is Markovian with additional structure that admits study via integrable probability techniques. In this talk\, I will discuss rece nt results on the Lyapunov exponents in the setting where the number M mat rix factors tend to infinity simultaneously with matrix sizes N. When this limit is tuned so that M and N grow on the same order\, the limiting Lyap unov exponents can be described in terms of Dyson Brownian motion with a s pecial drift vector\, which in turn can be linked to a matrix-valued diffu sion on the complex general linear group. We find that this description is universal\, under general assumptions on the spectrum of the matrix facto rs.\n LOCATION:https://researchseminars.org/talk/Probability/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Massimiliano Gubinelli (University of Bonn) DTSTART:20220502T201500Z DTEND:20220502T211500Z DTSTAMP:20260422T212558Z UID:Probability/48 DESCRIPTION:Title: What is stochastic quantization?\nby Massimiliano Gubinelli (Univ ersity of Bonn) as part of MIT probability seminar\n\n\nAbstract\nIn this talk I will introduce the idea of stochastic\nquantization from a mathemat ical perspective\, that is as a tool to\nanalyze rigorously Euclidean quan tum fields. I will show that there\nare several different "stochastic quan tizations” for which we will\nidentify common structures and ideas which take the form of a\nstochastic analysis of Euclidean quantum fields.\n LOCATION:https://researchseminars.org/talk/Probability/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Phil Sosoe (Cornell University) DTSTART:20220509T190000Z DTEND:20220509T200000Z DTSTAMP:20260422T212558Z UID:Probability/49 DESCRIPTION:Title: Almost-optimal regularity conditions in the CLT for Wigner matrices.< /a>\nby Phil Sosoe (Cornell University) as part of MIT probability seminar \n\nLecture held in Room 2-361 in the Simons Building.\n\nAbstract\nWe con sider linear spectral statistics for test functions of low regularity and Wigner matrices with smooth entry distribution. We show that for functions in the Sobolev space $H^{1/2 + \\epsilon}$ or the space $C^{1/2 + \\epsil on}$ that are supported within the spectral bulk of the semicircle distrib ution\, the variance remains bounded asymptotically. As a consequence\, th ese linear spectral statistics have asymptotic Gaussian fluctuations with the same variance as in the CLT for functions of higher regularity\, for a ny $\\epsilon > 0$. This result is nearly optimal in the sense that the va riance does remain bounded for functions in $H^{1/2}$\, and was previously known only for matrices in Gaussian Unitary Ensemble.\n LOCATION:https://researchseminars.org/talk/Probability/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Falconet (NYU) DTSTART:20220228T211500Z DTEND:20220228T221500Z DTSTAMP:20260422T212558Z UID:Probability/50 DESCRIPTION:Title: Metric growth dynamics in Liouville quantum gravity\nby Hugo Falc onet (NYU) as part of MIT probability seminar\n\n\nAbstract\n\\noindent Li ouville quantum gravity (LQG) is a canonical model of random geometry. Ass ociated with the planar Gaussian free field\, this geometry with special c onformal symmetries was introduced in the physics literature by Polyakov i n the 80's and is conjectured to describe the scaling limit of random plan ar maps. In this talk\, I will introduce LQG as a metric measure space and discuss recent results on the associated metric growth dynamics. The prim ary focus will be on the dynamics of the trace of the free field on the bo undary of growing LQG balls. \\\\\n\\vspace{2ex}\n\\noindent Based on a jo int work with Julien Dubédat.\n LOCATION:https://researchseminars.org/talk/Probability/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Eviatar Procaccia (Technion) DTSTART:20220314T170000Z DTEND:20220314T180000Z DTSTAMP:20260422T212558Z UID:Probability/51 DESCRIPTION:Title: Stationary Hastings-Levitov model\nby Eviatar Procaccia (Technion ) as part of MIT probability seminar\n\nLecture held in Room 2-132 in the Simons Building.\n\nAbstract\nWe construct and study a stationary version of the Hastings-Levitov(0) model. We prove that unlike the classical model \, in the stationary case\, particle sizes are tight\, yielding that this model can be seen as a tractable off-lattice Diffusion Limited Aggregation (DLA). The stationary setting together with a geometric interpretations o f the harmonic measure yields new geometric results such as finiteness of arms\, exact growth rate and fractal dimension equals 3/2\, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of D LA growing on a long line segment. We will also show that similar results can be achieved in a cylinder.\n LOCATION:https://researchseminars.org/talk/Probability/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Schmid (Princeton University) DTSTART:20220314T201500Z DTEND:20220314T211500Z DTSTAMP:20260422T212558Z UID:Probability/52 DESCRIPTION:Title: Mixing times for the TASEP on the circle\nby Dominik Schmid (Prin ceton University) as part of MIT probability seminar\n\nLecture held in Ro om 2-147 in the Simons Building.\n\nAbstract\nThe exclusion process is one of the best-studied examples of an interacting particle system. In this t alk\, we consider simple exclusion processes on finite graphs. We give an overview over some recent results on the mixing time of the totally asymme tric simple exclusion process (TASEP). In particular\, we provide bounds o n the mixing time of the TASEP on the circle\, using a connection to perio dic last passage percolation. This talk is based on joint work with Allan Sly (Princeton).\n LOCATION:https://researchseminars.org/talk/Probability/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Remi Rhodes (Aix-Marseille Université) DTSTART:20220425T170000Z DTEND:20220425T180000Z DTSTAMP:20260422T212558Z UID:Probability/53 DESCRIPTION:Title: Segal’s axioms and conformal bootstrap in Liouville theory\nb y Remi Rhodes (Aix-Marseille Université) as part of MIT probability semin ar\n\nLecture held in Room 2 - 361 in the Simons Building.\n\nAbstract\nCo nformal field theories (CFT) are expected to describe models of statistica l physics in 2D undergoing a second order phase transition at their critic al point. Several axiomatics have been proposed to lay the mathematical fo undations for the concept of CFT. In Segal’s approach\, the data for a CFT are an Hilbert space H and a map that associates to each Riemann surfa ce S with boundary a Hilbert-Schmidt operator (called amplitude) acting on the tensor product $H^b$ with b the number of boundary components of S. A mplitudes are then assumed to compose in a natural way under gluing of sur faces along their boundaries. Segal’s approach turned out to be very att ractive for mathematicians in view of its geometric flavor. Also\, it give s a geometrical way to understand the conformal bootstrap conjecture in ph ysics: correlation functions of CFT should factorize as an integral over t heir spectrum of the product of (squared) conformal blocks times the struc ture constants of the CFT (the 3 point correlation functions on the Rieman n sphere). Conformal blocks are holomorphic functions of the moduli of the space of Riemann surfaces with marked point\, which are universal in the sense that they only depend on the commutation relations of a given Lie al gebra\, the Virasoro algebra. Structure constants are model dependent. In this talk I will explain how this picture for CFTs drawn by Segal applies to Liouville theory (LCFT)\, which is a non rational conformal field theo ry developed in the early 80s in physics to describe random Riemannian metrics on Riemann surfaces.\n LOCATION:https://researchseminars.org/talk/Probability/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme Silva (University of Sao Paolo) DTSTART:20220912T201500Z DTEND:20220912T211500Z DTSTAMP:20260422T212558Z UID:Probability/54 DESCRIPTION:Title: Universality for a class of statistics of Hermitian random matrices a nd the integro-differential Painlevé II equation.\nby Guilherme Silva (University of Sao Paolo) as part of MIT probability seminar\n\n\nAbstrac t\nIt has been known since the 1990s that fluctuations of eigenvalues of r andom matrices\, when appropriately scaled and in the sense of one-point d istribution\, converge to the Airy2 point process in the large matrix limi t. In turn\, the latter can be described by the celebrated Tracy-Widom dis tribution.\n\nIn this talk we discuss recent findings of Ghosal and myself \, showing that certain statistics of eigenvalues also converge universali ty to appropriate statistics of the Airy2 point process\, interpolating be tween a hard and soft edge of eigenvalues. Such found statistics connect a lso to the integro-differential Painlevé II equation\, in analogy with th e celebrated Tracy-Widom connection between Painlevé II and the Airy2 pro cess.\n LOCATION:https://researchseminars.org/talk/Probability/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Mucciconi (University of Warwick) DTSTART:20220919T201500Z DTEND:20220919T211500Z DTSTAMP:20260422T212558Z UID:Probability/55 DESCRIPTION:Title: Title to be announced\nby Matteo Mucciconi (University of Warwick ) as part of MIT probability seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Probability/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Hough (Stony Brook University) DTSTART:20221031T201500Z DTEND:20221031T211500Z DTSTAMP:20260422T212558Z UID:Probability/56 DESCRIPTION:Title: Covering systems of congruences\nby Robert Hough (Stony Brook Uni versity) as part of MIT probability seminar\n\n\nAbstract\n\\noindent A di stinct covering system of congruences is a list of congruences\n\\[\na_i \ \bmod m_i\, \\qquad i = 1\, 2\, ...\, k\n\\]\nwhose union is the integers. Erd\\H{o}s asked if the least modulus $m_1$ of a distinct covering syste m of congruences can be arbitrarily large (the minimum modulus problem for covering systems\, \\$ 1000 ) and if there exist distinct covering system s of congruences all of whose moduli are odd (the odd problem for covering systems\, \\$ 25). I'll discuss my proof of a negative answer to the min imum modulus problem\, and a quantitative refinement with Pace Nielsen tha t proves that any distinct covering system of congruences has a modulus di visible by either 2 or 3. The proofs use the probabilistic method and in particular use a sequence of pseudorandom probability measures adapted to the covering process. Time permitting\, I may briefly discuss a reformula tion of our method due to Balister\, Bollob\\'{a}s\, Morris\, Sahasrabudhe and Tiba which solves a conjecture of Shinzel (any distinct covering syst em of congruences has one modulus that divides another) and gives a negati ve answer to the square-free version of the odd problem.\n LOCATION:https://researchseminars.org/talk/Probability/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandros Eskenazis (CNRS) DTSTART:20221003T201500Z DTEND:20221003T211500Z DTSTAMP:20260422T212558Z UID:Probability/57 DESCRIPTION:Title: Learning low-degree functions on the discrete hypercube\nby Alexa ndros Eskenazis (CNRS) as part of MIT probability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract\nLet f be an unknown fun ction on the n-dimensional discrete hypercube. How many values of f do we need in order to approximately reconstruct the function? In this talk we s hall discuss the random query model for this fundamental problem from comp utational learning theory. We will explain a newly discovered connection w ith a family of polynomial inequalities going back to Littlewood (1930) wh ich will in turn allow us to derive sharper estimates for the the query co mplexity of this model\, exponentially improving those which follow from t he classical Low-Degree Algorithm of Linial\, Mansour and Nisan (1989). Ti me permitting\, we will also show a matching information-theoretic lower b ound. Based on joint works with Paata Ivanisvili (UC Irvine) and Lauritz S treck (Cambridge).\n LOCATION:https://researchseminars.org/talk/Probability/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Hao Shen (UW-Madison) DTSTART:20221024T201500Z DTEND:20221024T211500Z DTSTAMP:20260422T212558Z UID:Probability/58 DESCRIPTION:Title: Stochastic Yang-Mills process in 2D and 3D.\nby Hao Shen (UW-Madi son) as part of MIT probability seminar\n\nLecture held in Room 2-147 in t he Simons Building.\n\nAbstract\nWe will discuss stochastic quantization o f the Yang-Mills model on two and three dimensional torus. In stochastic q uantization we consider the Langevin dynamic for the Yang-Mills model whic h is described by a stochastic PDE. We construct local solution to this SP DE and prove that the solution has a gauge invariant property in law\, whi ch then defines a Markov process on the space of gauge orbits. We will als o describe the construction of this orbit space\, on which we have well-de fined holonomies and Wilson loop observables. Based on joint work with Aja y Chandra\, Ilya Chevyrev\, and Martin Hairer.\n LOCATION:https://researchseminars.org/talk/Probability/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Dor Elboim (Princeton University) DTSTART:20221107T211500Z DTEND:20221107T221500Z DTSTAMP:20260422T212558Z UID:Probability/59 DESCRIPTION:Title: Infinite cycles in the interchange process in five dimensions\nby Dor Elboim (Princeton University) as part of MIT probability seminar\n\n\ nAbstract\n\\noindent In the interchange process on a graph G=(V\,E)\, the re is a particle on each vertex of the graph and an independent Poisson cl ock on each one of the edges. Once the clock of an edge rings\, the two pa rticles on the two sides of the edge switch. After time t\, the particles are permuted according to a random permutation $\\pi_t:V\\to V$. A famous conjecture of Balint Toth states that the following holds when $G=\\mathbb $ $Z^d$ :\n(1) If d=2\, then the permutation $\\pi_t$ contains only finite cycles for all t>0.\n(2) If $d\\ge 3$\, then there exists $t_c$ such that for $tt_c$\, $\\p i_t$ contains infinite cycles.\n\n\\vspace{2ex}\n\n\\noindent We prove the existence of infinite cycles for all $d\\ge 5$ and all $t$ sufficiently l arge. To this end\, we study the cyclic time random walk obtained by expos ing the cycle of the origin in $\\pi_t$. We show that this walk is diffusi ve using a multiscale inductive argument.\n\n\\vspace{2ex}\n\n\\noindent T his is a joint work with Allan Sly.\n LOCATION:https://researchseminars.org/talk/Probability/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Bailey (CUNY) DTSTART:20221121T211500Z DTEND:20221121T221500Z DTSTAMP:20260422T212558Z UID:Probability/60 DESCRIPTION:Title: Title to be announced\nby Emma Bailey (CUNY) as part of MIT proba bility seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Probability/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Hoi Nguyen (OSU) DTSTART:20221212T211500Z DTEND:20221212T221500Z DTSTAMP:20260422T212558Z UID:Probability/61 DESCRIPTION:Title: On roots of random trigonometric polynomials and related models\n by Hoi Nguyen (OSU) as part of MIT probability seminar\n\nLecture held in Room 2-147 in the Simons Building.\n\nAbstract\nIn this talk we will discu ss various basic statistics of the number of real roots of random trigonom etric polynomials\, as well as the minimum modulus and the nearest roots s tatistics to the unit circle of Kac polynomials. We emphasize the universa lity aspects of all these problems.\n\nBased on joint works with Cook\, Do \, O. Nguyen\, Yakir and Zeitouni\n LOCATION:https://researchseminars.org/talk/Probability/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Wang (MIT) DTSTART:20221114T211500Z DTEND:20221114T221500Z DTSTAMP:20260422T212558Z UID:Probability/62 DESCRIPTION:Title: Title to be announced\nby Sven Wang (MIT) as part of MIT probabil ity seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Probability/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Indigenous Peoples' Day (MIT) DTSTART:20221010T201500Z DTEND:20221010T211500Z DTSTAMP:20260422T212558Z UID:Probability/63 DESCRIPTION:Title: No Seminar On This Day\nby Indigenous Peoples' Day (MIT) as part of MIT probability seminar\n\n\nAbstract\nhttps://news.mit.edu/2022/indige nous-scholarship-mit-0425\n LOCATION:https://researchseminars.org/talk/Probability/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Sayan Das DTSTART:20221128T211500Z DTEND:20221128T221500Z DTSTAMP:20260422T212558Z UID:Probability/64 DESCRIPTION:by Sayan Das as part of MIT probability seminar\n\nAbstract: T BA\n LOCATION:https://researchseminars.org/talk/Probability/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Changji Xu DTSTART:20221205T211500Z DTEND:20221205T221500Z DTSTAMP:20260422T212558Z UID:Probability/65 DESCRIPTION:by Changji Xu as part of MIT probability seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Probability/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Remy (IAS\, Princeton) DTSTART:20221017T201500Z DTEND:20221017T211500Z DTSTAMP:20260422T212558Z UID:Probability/66 DESCRIPTION:Title: Modular transformation of conformal blocks via Liouville CFT\nby Guillaume Remy (IAS\, Princeton) as part of MIT probability seminar\n\nLec ture held in Room 2-147 in the Simons Building.\n\nAbstract\nConformal blo cks are objects of fundamental importance in mathematical physics. They ar e a key input to the conformal bootstrap program to exactly solve 2D confo rmal field theory (CFT) and are related to 4D supersymmetric gauge theory through the Alday-Gaiotto-Tachikawa correspondence. They are typically def ined as power series via the representation theory of the Virasoro algebra but in this talk we will provide novel probabilistic expressions using th e Gaussian free field. This will allow us to obtain many analytic properti es such as modular transformations. Our methods are based on recent develo pments in the probabilistic construction of the Liouville CFT\, a theory f irst introduced to describe random surfaces by A. Polyakov in the context of string theory. Based on joint work with Promit Ghosal\, Xin Sun\, and Y i Sun.​\n LOCATION:https://researchseminars.org/talk/Probability/66/ END:VEVENT END:VCALENDAR