BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ofer Zeitouni (Weizmann Institute of Science) DTSTART:20200420T113000Z DTEND:20200420T123000Z DTSTAMP:20260422T212832Z UID:HSPETDS/1 DESCRIPTION:Title: Stability and instability of spectrum for noisy perturbations of non-Hermi tian matrices\nby Ofer Zeitouni (Weizmann Institute of Science) as par t of Horowitz seminar on probability\, ergodic theory and dynamical system s\n\nLecture held in 309.\n\nAbstract\nWe discuss the spectrum of high dim ensional non-Hermitian matrices under small noisy perturbations. That spec trum can be extremely unstable\, as the maximal nilpotent matrix JN with J N(i\,j)=1 iff j=i+1 demonstrates. Numerical analysts studied worst case pe rturbations\, using the notion of pseudo-spectrum. Our focus is on finding the locus of most eigenvalues (limits of density of states)\, as well as studying stray eigenvalues ("outliers"). I will describe the background\, show some fun and intriguing simulations\, and present some theorems and w ork in progress concerning eigenvectors. No background will be assumed. Th e talk is based on joint work with Anirban Basak\, Elliot Paquette\, and M artin Vogel.\n LOCATION:https://researchseminars.org/talk/HSPETDS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Tal Orenshtein (TU Berlin\, Weierstrass Institute and Free Univers ity of Berlin) DTSTART:20200427T113000Z DTEND:20200427T123000Z DTSTAMP:20260422T212832Z UID:HSPETDS/2 DESCRIPTION:Title: Rough walks in random environment\nby Tal Orenshtein (TU Berlin\, Weie rstrass Institute and Free University of Berlin) as part of Horowitz semin ar on probability\, ergodic theory and dynamical systems\n\nLecture held i n 309.\n\nAbstract\nRandom walks in random environment have been extensive ly studied in the last half-century and invariance principles are known to hold in various cases. We shall discuss recent contributions\, where the scaling limit is obtained in the rough path space for the lifted random wa lk. Except for the immediate application to stochastic differential equati ons\, this provides new information on the structure of the limiting path - an enhanced Brownian motion with a linearly perturbed second level\, whi ch is characterized in various ways. Time permitting\, we shall elaborate on the main tools to tackle these problems. Based on joint works with Olga Lopusanschi\, with Jean-Dominique Deuschel and Nicolas Perkowski and with Johaness Bäumler\, Noam Berger and Martin Slowik.\n LOCATION:https://researchseminars.org/talk/HSPETDS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Garban (Université Lyon 1) DTSTART:20200504T113000Z DTEND:20200504T123000Z DTSTAMP:20260422T212832Z UID:HSPETDS/4 DESCRIPTION:Title: Kosterlitz-Thouless transition and statistical reconstruction of the Gauss ian free field\nby Christophe Garban (Université Lyon 1) as part of H orowitz seminar on probability\, ergodic theory and dynamical systems\n\nL ecture held in 309.\n\nAbstract\nThe Berezinskii-Kosterlitz-Thouless trans ition (BKT transition) is a phase transition which occurs in dimension two for spin systems such as the plane rotator model (or XY model). This phas e transition was discovered by these three physicists as the first example of a topological phase transition and was rigorously understood by Fröhl ich and Spencer in the 80's. I will spend the main part of my talk explain ing what are these topological phase transitions. I will then survey the c ontributions of Fröhlich and Spencer to this theory and I will end with n ew results we obtained recently with Avelio Sepúlveda in this direction.\ nThe talk will be based mostly on the preprint: https://arxiv.org/abs/2002 .12284\n LOCATION:https://researchseminars.org/talk/HSPETDS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Renan Gross (Weizmann Institute) DTSTART:20200511T113000Z DTEND:20200511T123000Z DTSTAMP:20260422T212832Z UID:HSPETDS/5 DESCRIPTION:Title: Stochastic processes for Boolean profit\nby Renan Gross (Weizmann Inst itute) as part of Horowitz seminar on probability\, ergodic theory and dyn amical systems\n\nLecture held in 309.\n\nAbstract\nNot even influence ine qualities for Boolean functions can escape the long arm of stochastic proc esses. I will present a (relatively) natural stochastic process which turn s Boolean functions and their derivatives into jump-process martingales. T here is much to profit from analyzing the individual paths of these proces ses: Using stopping times and level inequalities\, we will prove a conject ure of Talagrand relating edge boundaries and the influences\, and show st ability of KKL\, isoperimetric\, and Talagrand's influence inequality. The technique (mostly) bypasses hypercontractivity. Work with Ronen Eldan.\n LOCATION:https://researchseminars.org/talk/HSPETDS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Izabella Stuhl (Penn State University) DTSTART:20200518T120000Z DTEND:20200518T130000Z DTSTAMP:20260422T212832Z UID:HSPETDS/6 DESCRIPTION:Title: The hard-core model in discrete 2D\nby Izabella Stuhl (Penn State Univ ersity) as part of Horowitz seminar on probability\, ergodic theory and dy namical systems\n\n\nAbstract\nThe hard-core model describes a system of n on-overlapping identical hard spheres in a space or on a lattice (more gen erally\, on a graph). An interesting open problem is: do hard disks in a p lane admit a unique Gibbs measure at high density? It seems natural to app roach this question by possible discrete approximations where disks must h ave the centers at sites of a lattice or vertices of a graph.\n\nIn this t alk\, I will report on progress achieved for the models on a unit triangul ar lattice $\\mathbb{A}_2$\, square lattice $\\mathbb{Z}^2$ and a honeycom b graph $\\mathbb{H}_2$ for a general value of disk diameter $D$ (in the E uclidean metric). We analyze the structure of Gibbs measures for large fug acities (i.e.\, high densities) by means of the Pirogov-Sinai theory and i ts modifications. It connects extreme Gibbs measures with dominant ground states.\n\nOn $\\mathbb{A}_2$ we give a complete description of the set of extreme Gibbs measures\; the answer is provided in terms of the prime dec omposition of the Löschian number $D^2$ in the Eisenstein integer ring. O n $\\mathbb{Z}^2$\, we work with Gaussian numbers. Here we have to exclude a finite collection of values of $D$ with sliding\; for the remaining exc lusion distances the answer is given in terms of solutions to a discrete m inimization problem. The latter is connected to norm equations in the cycl otomic integer ring $\\mathbb{Z}[\\zeta]$\, where $\\zeta$ is a primitive 12th root of unity. On $\\mathbb{H}_2$\, we employ connections with the mo del on $\\mathbb{A}_2$\, although there are some exceptional values requir ing a special approach.\n\nParts of our argument contain computer-assisted proofs: identification of instances of sliding\, resolution of dominance issues. This is a joint work with A. Mazel and Y. Suhov.\n LOCATION:https://researchseminars.org/talk/HSPETDS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Dario (Tel Aviv University) DTSTART:20200525T120000Z DTEND:20200525T130000Z DTSTAMP:20260422T212832Z UID:HSPETDS/7 DESCRIPTION:Title: Large-scale behavior of the Villain model at low temperature in d = 3\ nby Paul Dario (Tel Aviv University) as part of Horowitz seminar on probab ility\, ergodic theory and dynamical systems\n\n\nAbstract\nIn this talk\, we will study the Villain rotator model in dimension three and prove that \, at low temperature\, the truncated two-point function of the model deca ys asymptotically like $|x|^{2-d}$\, with an algebraic rate of convergence . The argument starts from the observation that the asymptotic properties of the Villain model are related to the large-scale behavior of a vector-v alued random surface with uniformly elliptic and infinite range potential\ , following the arguments of Fröhlich\, Spencer and Bauerschmidt. We will then see that this behavior can be studied quantitatively by combining tw o sets of tools: the Helffer-Sjöstrand PDE\, initially introduced by Nadd af and Spencer to identify the scaling limit of the discrete Ginzburg-Land au model\, and the techniques of the quantitative theory of stochastic hom ogenization developed by Armstrong\, Kuusi and Mourrat. Joint work with We i Wu.\n LOCATION:https://researchseminars.org/talk/HSPETDS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ofir Gorodetsky (Tel Aviv University) DTSTART:20200316T123000Z DTEND:20200316T133000Z DTSTAMP:20260422T212832Z UID:HSPETDS/9 DESCRIPTION:Title: The anatomy of integers and Ewens permutations\nby Ofir Gorodetsky (Te l Aviv University) as part of Horowitz seminar on probability\, ergodic th eory and dynamical systems\n\n\nAbstract\nWe will discuss an analogy betwe en integers and permutations\, an analogy which goes back to works of Erd ős and Kac and of Billingsley which we shall survey. Certain statistics o f the prime factors of a uniformly drawn integer (between $1$ and $x$) agr ee\, in the limit\, with similar statistics of the cycles of a uniformly d rawn permutation from the symmetric group on $n$ elements. This analogy is beneficial to both number theory and probability theory\, as one can ofte n prove new number-theoretical results by employing probabilistic ideas\, and vice versa.\nThe Ewens measure with parameter Θ\, first discovered in the context of population genetics\, is a non-uniform measure on permutat ions. We will present an analogue of this measure on the integers\, and sh ow how natural questions on the integers have answers which agree with ana logous problems for the Ewens measure. For example\, the size of the prime factors of integers which are sums of two squares\, and the cycle lengths of permutations drawn according to the Ewens measure with parameter 1/2\, both converge to the Poisson-Dirichlet process with parameter 1/2. We wil l convey some of the ideas behind the proofs.\nJoint work with Dor Elboim. \n LOCATION:https://researchseminars.org/talk/HSPETDS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Matan Seidel (Tel Aviv University) DTSTART:20200323T123000Z DTEND:20200323T133000Z DTSTAMP:20260422T212832Z UID:HSPETDS/10 DESCRIPTION:Title: Random walks on circle packings\nby Matan Seidel (Tel Aviv University ) as part of Horowitz seminar on probability\, ergodic theory and dynamica l systems\n\n\nAbstract\nA circle packing is a canonical way of representi ng a planar graph. There is a deep connection between the geometry of the circle packing and the probabilistic property of recurrence/transience of the simple random walk on the underlying graph\, as shown in the famous He -Schramm Theorem. The removal of one of the Theorem's assumptions - that o f bounded degrees - can cause the theorem to fail. However\, by using cert ain natural weights that arise from the circle packing for a weighted rand om walk\, (at least) one of the directions of the He-Schramm Theorem remai ns true. In the talk I will present some of the theory of circle packings and random walks and discuss some of the ideas used in the proof. Joint wo rk with Ori Gurel-Gurevich.\n LOCATION:https://researchseminars.org/talk/HSPETDS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathanaël Berestycki (University of Vienna) DTSTART:20200330T113000Z DTEND:20200330T123000Z DTSTAMP:20260422T212832Z UID:HSPETDS/11 DESCRIPTION:Title: Random walks on random planar maps and Liouville Brownian motion\nby Nathanaël Berestycki (University of Vienna) as part of Horowitz seminar o n probability\, ergodic theory and dynamical systems\n\n\nAbstract\nThe st udy of random walks on random planar maps was initiated in a series of sem inal papers of Benjamini and Schramm at the end of the 90s\, motivated by contemporary (nonrigourous) works in the study of Liouville Quantum Gravit y (LQG). Both topics have been the subject of intense research following r emarkable breakthroughs in the last few years.\n\nAfter reviewing some of the recent developments in these fields - including Liouville Brownian mot ion\, a canonical notion of diffusion on LQG surfaces - I will describe so me joint work with Ewain Gwynne. In this work we show that random walks on certain models of random planar maps (known as mated-CRT planar maps) hav e a scaling limit given by Liouville Brownian motion. This is true whether the maps are embedded using SLE/LQG theory or more intrinsically using th e Tutte embedding. This is the first result confirming that Liouville Brow nian motion is the scaling limit of random walks on random planar maps.\n\ nThe proof relies on some earlier work of Gwynne\, Miller and Sheffield wh ich proves convergence to Brownian motion\, modulo time-parametrisation. A s an intermediate result of independent interest\, we derive an axiomatic characterisation of Liouville Brownian motion\, for which the notion of Re vuz measure of a Markov process plays a crucial role.\n LOCATION:https://researchseminars.org/talk/HSPETDS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Chelkak (École Normale Supérieure Paris and St. Petersbur g Dept. of Steklov Institute RAS) DTSTART:20200601T120000Z DTEND:20200601T130000Z DTSTAMP:20260422T212832Z UID:HSPETDS/12 DESCRIPTION:Title: Bipartite dimer model: Gaussian Free Field on Lorentz-minimal surfaces\nby Dmitry Chelkak (École Normale Supérieure Paris and St. Petersburg Dept. of Steklov Institute RAS) as part of Horowitz seminar on probability \, ergodic theory and dynamical systems\n\n\nAbstract\nWe discuss a new vi ewpoint on the convergence of fluctuations in the bipartite dimer model co nsidered on big planar graphs. Classically\, when these graphs are parts o f refining lattices\, the boundary profile of the height function and a la ttice-dependent entropy functional are responsible for the conformal struc ture\, in which the limiting GFF (and CLE(4)) should be defined. Motivated by a long-term perspective of understanding the `discrete conformal struc ture’ of random planar maps equipped with the dimer (or the critical Isi ng) model\, we introduce `perfect t-embeddings’ of abstract weighted bip artite graphs and argue that such embeddings reveal the conformal structur e in a universal way: as that of a related Lorentz-minimal surface in 2+1 (or 2+2) dimensions.\n\nThough the whole concept is very new\, concrete de terministic examples (e.g\, the Aztec diamond) justify its relevance\, and general convergence theorems obtained so far are of their own interest. S till\, many open questions remain\, one of the key ones being to understan d the mechanism behind the appearance of the Lorentz metric in this classi cal problem.\n\nBased upon recent joint works with Benoît Laslier\, Sanja y Ramassamy and Marianna Russkikh.\n LOCATION:https://researchseminars.org/talk/HSPETDS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Thierry Bodineau (École Polytechnique) DTSTART:20200608T120000Z DTEND:20200608T130000Z DTSTAMP:20260422T212832Z UID:HSPETDS/13 DESCRIPTION:Title: Fluctuating Boltzmann equation and large deviations for a hard sphere gas \nby Thierry Bodineau (École Polytechnique) as part of Horowitz semin ar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nSi nce the seminal work of Lanford\, the convergence of the hard-sphere dynam ics towards the Boltzmann equation has been established in a dilute gas as ymptotic. In this talk\, we are going to discuss the fluctuations of this microscopic dynamics around the Boltzmann equation and the convergence of the fluctuation field to a generalised Ornstein-Uhlenbeck process. We will show also that the occurrence of atypical evolutions can be quantified by a large deviation principle. This analysis relies on the study of the cor relations created by the Hamiltonian dynamics. We will see that the emerge nce of irreversibility in the kinetic limit can be related to the singular ity of these correlations.\n LOCATION:https://researchseminars.org/talk/HSPETDS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Osama Khalil (University of Utah) DTSTART:20200615T140000Z DTEND:20200615T150000Z DTSTAMP:20260422T212832Z UID:HSPETDS/14 DESCRIPTION:Title: Singular Vectors on Fractals and Homogeneous Flows\nby Osama Khalil ( University of Utah) as part of Horowitz seminar on probability\, ergodic t heory and dynamical systems\n\n\nAbstract\nThe theory of Diophantine appro ximation is underpinned by Dirichlet’s fundamental theorem. Broadly spea king\, the main questions in the theory concern quantifying the prevalence of points with exceptional behavior with respect to Dirichlet’s result. The work of Dani and Kleinbock-Margulis connects these questions to the r ecurrence behavior of certain flows on homogeneous spaces. For example\, d ivergent orbits of such flows correspond to so-called singular vectors. Af ter a brief overview of the subject and the motivating questions\, I will discuss new results giving a sharp upper bound on the Hausdorff dimension of divergent orbits of certain diagonal flows emanating from fractals on t he space of unimodular lattices. Time permitting\, connections to the theo ry of projections of self-similar measures will be presented.\n LOCATION:https://researchseminars.org/talk/HSPETDS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Tyler Helmuth (University of Bristol) DTSTART:20200622T120000Z DTEND:20200622T130000Z DTSTAMP:20260422T212832Z UID:HSPETDS/15 DESCRIPTION:Title: Random spanning forests and hyperbolic symmetry\nby Tyler Helmuth (Un iversity of Bristol) as part of Horowitz seminar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nThe arboreal gas is the probab ility measure that arises from conditioning the random subgraph given by B ernoulli($p$) bond percolation to be a spanning forest\, i.e.\, to contain no cycles. This conditioning makes sense on any finite graph $G$\, and in the case $p=1/2$ gives the uniform measure on spanning forests. The arbor eal gas also arises as a $q\\to0$ limit of the $q$-state random cluster mo del.\n\nWhat are the percolative properties of these forests? This turns o ut to be a surprisingly rich question\, and I will discuss what is known a nd conjectured. I will also describe a tool for studying connection probab ilities\, the magic formula\, which arises due to an important connection between the arboreal gas and spin systems with hyperbolic symmetry.\n\nBas ed on joint work with Roland Bauerschmidt\, Nick Crawford\, and Andrew Swa n.\n LOCATION:https://researchseminars.org/talk/HSPETDS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaar Solomon (Ben-Gurion university of the Negev) DTSTART:20200629T120000Z DTEND:20200629T130000Z DTSTAMP:20260422T212832Z UID:HSPETDS/16 DESCRIPTION:Title: Bounded-displacement non-equivalence in substitution tilings\nby Yaar Solomon (Ben-Gurion university of the Negev) as part of Horowitz seminar on probability\, ergodic theory and dynamical systems\n\n\nAbstract\nGiven two Delone sets $Y$ and $Z$ in $R^d$ we study the existence of a bounded- displacement (BD) map between them\, namely a bijection $f$ from $Y$ to $Z $ so that the quantity $\\|y-f(y)\\|$\, $y\\in Y$\, is bounded. This notio n induces an equivalence relation on collections $X$ of Delone sets and we study the cardinality of BD($X$)\, a collection of all BD-class represent atives. In this talk we focus on sets $X$ of point sets that correspond to tilings in a substitution tiling space. We provide a sufficient condition under which |BD($X$)| is the continuum. In particular we show that\, in t he context of primitive substitution tilings\, |BD($X$)| can be greater th an $1$.\n LOCATION:https://researchseminars.org/talk/HSPETDS/16/ END:VEVENT END:VCALENDAR