Difference between revisions of "Past Probability Seminars Spring 2020"
(→April 30, 2020, Will Perkins (University of Illinois at Chicago)) 
m (Vadicgor moved page Probability Seminar to Past Probability Seminars Spring 2020) 
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Latest revision as of 16:18, 12 August 2020
Spring 2020
Thursdays in 901 Van Vleck Hall at 2:30 PM, unless otherwise noted. We usually end for questions at 3:20 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to joinprobsem@lists.wisc.edu
January 23, 2020, Timo Seppalainen (UW Madison)
Nonexistence of biinfinite geodesics in the exponential corner growth model
Whether biinfinite geodesics exist has been a significant open problem in first and lastpassage percolation since the mid80s. A nonexistence proof in the case of directed planar lastpassage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and incrementstationary lastpassage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).
January 30, 2020, Scott Smith (UW Madison)
Quasilinear parabolic equations with singular forcing
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by spacetime white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasilinear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counterterms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.
February 6, 2020, CheukYin Lee (Michigan State)
Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or selfintersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.
February 13, 2020, Jelena Diakonikolas (UW Madison)
Langevin Monte Carlo Without Smoothness
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradientLipschitz) logdensities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomialtime convergence guarantees for a variant of LMC in the setting of nonsmooth logconcave distributions. At a high level, our results follow by leveraging the implicit smoothing of the logdensity that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation. Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.
February 20, 2020, Philip Matchett Wood (UC Berkeley)
A replacement principle for perturbations of nonnormal matrices
There are certain nonnormal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of nongaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.
February 27, 2020, No seminar
March 5, 2020, Jiaoyang Huang (IAS)
Large Deviation Principles via Spherical Integrals
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;
4) the large deviation upper bound for the LittlewoodRichardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.
This is a joint work with Belinschi and Guionnet.
March 12, 2020, No seminar
March 19, 2020, Spring break
March 26, 2020, CANCELLED, Philippe Sosoe (Cornell)
April 2, 2020, CANCELLED, Tianyu Liu (UW Madison)
April 9, 2020, CANCELLED, Alexander Dunlap (Stanford)
April 16, 2020, CANCELLED, Jian Ding (University of Pennsylvania)
April 2224, 2020, CANCELLED, FRG Integrable Probability meeting
3day event in Van Vleck 911
April 23, 2020, CANCELLED, Martin Hairer (Imperial College)
Wolfgang Wasow Lecture at 4pm in Van Vleck 911
April 30, 2020, CANCELLED, Will Perkins (University of Illinois at Chicago)