Seminars and Colloquia by Series

TBA

Series
Algebra Student Seminar
Time
Friday, November 5, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skile 005
Speaker
Ian LewisGeorgia Tech

Gibbsian line ensembles and beta-corners processes

Series
Stochastics Seminar
Time
Thursday, November 4, 2021 - 16:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Evgeni DimitrovColumbia University

Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability.
Gibbsian line ensembles can be thought of as collections of finite or countably infinite independent random walkers whose distribution is reweighed by the sum of local interactions between the walkers. I will discuss some recent progress in the asymptotic study of Gibbsian line ensembles, summarizing some joint works with Barraquand, Corwin, Matetski, Wu and others.
Beta-corners processes are Gibbs measures on triangular arrays of interacting particles and can be thought of as analogues/extensions of multi-level spectral measures of random matrices. I will discuss some recent progress on establishing the global asymptotic behavior of beta-corners processes, summarizing some joint works with Das and Knizel.

TBA

Series
Algebra Seminar
Time
Tuesday, November 2, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jose RodriguezUniversity of Wisconsin, Madison

Spectral Theory for Products of Many Large Gaussian Matrices

Series
CDSNS Colloquium
Time
Friday, October 29, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Boris HaninPrinceton University

Please Note: Zoom link: https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

Let X_{N,n} be an iid product of N real Gaussian matrices of size n x n. In this talk, I will explain some recent joint work with G. Paouris 
(arXiv:2005.08899) about a non-asymptotic analysis of the singular values of X_{N,n} . I will begin by giving some intuition and motivation for studying such matrix products. Then, I will explain two new results. The first gives a rate of convergence for the global distribution of singular values of X_{N,n} to the so-called Triangle Law in the limit where N,n tend to infinity. The second is a kind of quantitative version of the multiplicative ergodic theorem, giving estimates at finite but large N on the distance between the joint distribution of all Lyapunov exponents of X_{N,n} and appropriately normalized independent Gaussians in the near-ergodic regime (N >> n).

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