BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sarai Hernandez (Technion) DTSTART:20200921T201500Z DTEND:20200921T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/1 DESCRIPTION:Title: Scaling limits of uniform spanning trees in three dimensions\nb y Sarai Hernandez (Technion) as part of IUB Probability seminar\n\nAbstrac t: TBA\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Chaojie Yuan (Indiana University) DTSTART:20200928T201500Z DTEND:20200928T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/2 DESCRIPTION:Title: Low variance couplings for stochastic models of intracellular proce sses with time-dependent rate functions\nby Chaojie Yuan (Indiana Univ ersity) as part of IUB Probability seminar\n\n\nAbstract\nA number of coup ling strategies are first presented for stochastically modeled biochemical processes with time-dependent parameters. In particular\, the stacked cou pling is introduced and is shown to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expect ations via multilevel Monte Carlo methods. \n\nAnalytical results related to this coupling is then derived in the context of Parametric Sensitivity Analysis. Such results are sparse\, and previous analysis utilizes a globa l Lipschitz assumption\, which is only applicable to a small percentage of the models found in the literature. We will extend the analysis to allow for (1) Locally Lipschitz intensity functions\, and (2) time dependence in the parameters. In particular\, binary systems\, a class of models that a ccounts for the vast majority of systems considered in the literature\, sa tisfy the assumptions of our theory. This is joint work with David Anderso n.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Mykhaylo Shkolnikov (Princeton University) DTSTART:20201005T201500Z DTEND:20201005T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/3 DESCRIPTION:Title: The supercooled Stefan problem\nby Mykhaylo Shkolnikov (Princet on University) as part of IUB Probability seminar\n\n\nAbstract\nThe Stefa n problem arising from the physics of supercooled liquids poses major math ematical challenges due to the presence of blow-ups\, including even the d efinition of solutions. I will explain how the problem can be reformulated in probabilistic terms and how related particle system models lead to an appropriate notion of a solution. The solutions can be then studied by pro babilistic techniques and a sharp description of the blow-ups can be estab lished. Based on joint works with Francois Delarue and Sergey Nadtochiy.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarai Hernandez Torres (Technion – Israel Institute of Technolog y) DTSTART:20201012T201500Z DTEND:20201012T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/4 DESCRIPTION:Title: Chase-escape with death\nby Sarai Hernandez Torres (Technion – Israel Institute of Technology) as part of IUB Probability seminar\n\n \nAbstract\nChase-escape is a competitive growth process in which red part icles spread to adjacent uncolored sites while blue particles overtake adj acent red particles. We can think of this model as rabbits escaping from w olves pursuing them on an infinite graph. There are two phases for chase-e scape. If the rabbits spread fast enough\, then both species coexist at an y time. Otherwise\, the wolves eat all the rabbits in a finite time. This talk presents a modification of chase-escape where each rabbit has a rando m lifespan\, after which it dies. When the underlying graph is a d-ary tre e\, chase-escape with death exhibits a new phase where death benefits the survival of the rabbit population. We will understand the phase transition s of this process through a connection between probability and analytic co mbinatorics. This is a joint work with Erin Beckman\, Keisha Cook\, Nicole Eikmeier\, and Matthew Junge.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ching Wei Ho (Indiana University) DTSTART:20201109T211500Z DTEND:20201109T220500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/5 DESCRIPTION:Title: The eigenvalues of the sum of a Hermitian matrix and an imaginary m ultiple of the GUE\nby Ching Wei Ho (Indiana University) as part of IU B Probability seminar\n\n\nAbstract\nIn 1955\, Wigner computed that the li miting eigenvalue distribution of the Gaussian unitary ensemble (GUE) is t he semicircle law. Random matrix theory then has been under development fo r decades\; remarkably\, in the 90s\, Voiculescu discovered that free prob ability theory can be used to study random matrices. In this talk\, I will speak on my recent work with Brian Hall\, where we use free probability t o compute the limiting eigenvalue distribution of the sum of a determinist ic Hermitian matrix and an imaginary multiple of a GUE. Unless the Hermiti an matrix is a zero matrix\, this random matrix is almost surely non-norma l.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shuwen Lou (Loyola University) DTSTART:20201116T211500Z DTEND:20201116T220500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/6 DESCRIPTION:Title: Distorted Brownian motion on spaces with varying dimension\nby Shuwen Lou (Loyola University) as part of IUB Probability seminar\n\n\nAbs tract\nWe introduce "distorted Brownian motion" (dBM) on a state space wit h varying dimension. Roughly speaking\, the state space consists of two co mponents: a 3-dimensional component and a 1-dimensional component. These t wo parts are joined together at the origin. The restriction of dBM on the 3-d component models a homopolymer with attractive potential at the origin . The restriction of dBM on the 1-d component can be any diffusion satisfy ing typical regularity conditions. We will discuss several properties of s uch processes\, including whether they are transient/recurrent\, the corre sponding radial process\, characterization via h-transform\, and their den sity estimates.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Curien DTSTART:20201130T150000Z DTEND:20201130T160000Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/7 DESCRIPTION:Title: Unraveling parking on random trees via random graphs\nby Nicola s Curien as part of IUB Probability seminar\n\n\nAbstract\nImagine a plane tree together with a configuration of particles (cars) at each vertex. Ea ch car tries to park on its node\, and if the latter is occupied\, it move s downward towards the root trying to find an empty slot. When the underly ing plane tree is a critical Galton--Watson conditioned to be large\, and when the car arrivals are i.i.d. on each vertex\, we observe a phase trans ition:\n- when the density of cars is small enough\, all but a few manage to park safely\,\n- whereas when the density of cars is high enough\, a po sitive fraction of them do not manage to park and exit through the root of the tree.\nThe critical density is an explicit function of the first two moments of the offspring distribution and cars arrivals (C. & Hénard 2019 ). We shall give a new point of view on this process by coupling it with t he ubiquitous Erdös--Rényi random graph process. This enables us to full y understand the (dynamical) phase transition in the scaling limit by rela ting it to the multiplicative coalescent process.\nThe talk is based on a joint work with Olivier Hénard and an ongoing project with Alice Contat.\ n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Timar DTSTART:20210322T201500Z DTEND:20210322T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/9 DESCRIPTION:Title: The Free Uniform Spanning Forest is disconnected in some virtually free groups\, depending on the generating set\nby Adam Timar as part o f IUB Probability seminar\n\n\nAbstract\nThe uniform measure on the set of all spanning trees of a finite graph is a classical object in probability . In an infinite graph\, one can take an exhaustion by finite subgraphs\, with some boundary conditions\, and take the limit measure. The Free Unifo rm Spanning Forest (FUSF) is one of the natural limits\, but it is less un derstood than the wired version\, the WUSF. If we take a finitely generate d group\, then several properties of WUSF and FUSF have been known to be i ndependent of the chosen Cayley graph of the group. Lyons and Peres asked if the number of trees in the FUSF is such.\n\nIn a joint work with Gabor Pete we give two different Cayley graphs of the same group such that the F USF is connected in one of them and it has infinitely many trees in the ot her. Furthermore\, since our example is a virtually free group\, we obtain ed a counterexample to the general expectation\, explicitly conjectured by Tang\, that such "tree-like" graphs would have connected FUSF. Several op en questions are inspired by the results. I will also present some prelimi nary results and conjectures on phase transition phenomena that happen if we put conductances on the edges of the underlying graph. These latter are joint work with Alexy\, Borbenyi and Imolay.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Muruhan Rathinam DTSTART:20210315T201500Z DTEND:20210315T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/10 DESCRIPTION:Title: Scaling limits for Random Walks on Graphs Embedded in the Euclidea n Space : An Approach to Model and Predict Macroscale Transport\nby Mu ruhan Rathinam as part of IUB Probability seminar\n\n\nAbstract\nWe propos e random walks on suitably defined graphs as a framework for finescale\nmo deling of particle motion in an obstructed environment. This motivates our \nstudy of a periodic\, directed and weighted graph embedded in a Euclidea n space\nand the scaling limit of the associated continuous time random wa lk on the\ngraph's nodes which jumps along the graph's edges with jump rat es given by\nthe edge weights.\nWe show that a suitably scaled version of the process converges to a linear\ndrift\, and the case of interest to us is that of null drift. In this case\, we\nshow that a suitably rescaled pr ocess converges weakly to\na Brownian motion. The diffusivity of the limit ing Brownian motion can be\ncomputed by solving a set of linear algebra pr oblems. These linear algebra\nproblems are analogous to the unit-cell prob lems in the homogenization theory \nfor PDEs. In the case of reversible ra tes\, we provide a variational\ncharacterization of the effective diffusiv ity analogous to the case of\nhomogenization theory for the diffusion PDE. This characterization makes use\nof vector calculus on graphs. \n \nWe al so present some sufficient conditions for null drift that include certain\ nsymmetries of the graph. Time permitting\, we discuss multiscale random w alks\nwhere in some parts of the space the jump rates are much slower (but non-zero).\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Damron (Georgia Institute of Technology) DTSTART:20210301T211500Z DTEND:20210301T220500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/11 DESCRIPTION:Title: Critical first-passage percolation in two dimensions\nby Micha el Damron (Georgia Institute of Technology) as part of IUB Probability sem inar\n\n\nAbstract\nIn 2d first-passage percolation (FPP)\, we place nonne gative i.i.d. weights (t_e) on the edges of Z^2 and study the induced weig hted graph pseudometric T = T(x\,y). If we denote by p = P(t_e = 0)\, then there is a transition in the large-scale behavior of the model as p varie s from 0 to 1. When p < 1/2\, T(0\,x) grows linearly in x\, and when p > 1 /2\, it is stochastically bounded. The critical case\, where p = 1/2\, is more subtle\, and the sublinear growth of T(0\,x) depends on the behavior of the distribution function of t_e near zero. I will discuss my work over the past few years that (a) determines the exact rate of growth of T(0\,x )\, (b) determines the "time constant" for the site-FPP model on the trian gular lattice and\, more recently (c) studies the growth of T(0\,x) in a d ynamical version of the model\, where weights are resampled according to i ndependent exponential clocks. These are joint works with J. Hanson\, D. H arper\, W.-K. Lam\, P. Tang\, and X. Wang.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawley DTSTART:20210426T201500Z DTEND:20210426T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/12 DESCRIPTION:Title: Extreme first passage times of normal and anomalous diffusion\ nby Sean Lawley as part of IUB Probability seminar\n\n\nAbstract\nWhy do 3 00 million sperm cells search for the oocyte in human fertilization when o nly a single sperm cell is necessary? Why do 1000 calcium ions enter a den dritic spine when only two ions are necessary to activate the relevant rec eptors? The seeming redundancy in these and other biological systems can b e understood in terms of extreme first passage time (FPT) theory.\n\nWhile FPT theory is often used to estimate timescales in biology\, the overwhel ming majority of studies focus on the time it takes a given single searche r to find a target. However\, in many scenarios the more relevant timescal e is the FPT of the first searcher to find a target from a large group of searchers. This fastest or extreme FPT depends on rare events and is often orders of magnitude faster than the FPT of a given single searcher. In th is talk\, we will explain recent results in extreme FPT theory and show ho w they modify traditional notions of diffusion timescales.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Gonzalez-Casanova DTSTART:20210412T201500Z DTEND:20210412T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/13 DESCRIPTION:Title: From continuous state branching processes to coalescents\nby A drian Gonzalez-Casanova as part of IUB Probability seminar\n\n\nAbstract\n The relation between these two important families of processes has been in vestigated in some cases. For example\, in a a renowned paper by seven aut hors\, the $\\beta$-coalescents are obtained as a functional of two indep endent $\\alpha$-stable branching processes. Using Gillispie's sampling me thod\, we find that an analogous relation holds for every Lambda coalescen t. Furthermore\, functionals of independent CSBPs with different laws lead to frequency processes of coalescents with selection\, mutation\, efficie ncy and more. This is a joint work in progress with Maria Emilia Caballero (UNAM) and Jose Luis Perez (CIMAT).\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Hughes DTSTART:20210517T201500Z DTEND:20210517T210500Z DTSTAMP:20260422T225657Z UID:ProbabilityIUB/14 DESCRIPTION:Title: New path properties for measure-valued Markov processes\nby Th omas Hughes as part of IUB Probability seminar\n\n\nAbstract\nAbstract: I will discuss support and path properties for measure-valued Markov process es. My main focus will be some new results about the density of the (α\,d \,β)-superprocess\, a spatial branching model associated to an α-stable spatial motion in d dimensions and a (1+β)-stable branching mechanism. Th ese include (i) strict positivity of the density at a fixed time (for cert ain values of α and β) and (ii) a classification of the measures which t he density “charges” almost surely\, and of the measures which the den sity fails to charge with positive probability\, when conditioned on survi val. The duality between the superprocess and a fractional PDE is central to our method\, and I will discuss how the probabilistic statements above correspond to new results about solutions to the PDE. \n\nIf time permits\ , I will also discuss work with Ed Perkins on super-Brownian motion\, and recent work-in-progress with Xiaowen Zhou on the Fleming-Viot model.\n LOCATION:https://researchseminars.org/talk/ProbabilityIUB/14/ END:VEVENT END:VCALENDAR