Gibbsian line ensembles and beta-corners processes

The Department of Mathematics in the College of Arts and Sciences is honored to welcome Dr. Evgeni Dimitrov to deliver the weekly colloquium. Dr. Dimitrov is a Joseph F. Ritt Assistant Professor at Columbia University, where he works in asymptotic analysis of stochastic integrable systems via hybrid methods that lie on the interface of representation theory, analysis and combinatorics.

Abstract: 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.

For Zoom link, please email laquinon@syr.edu.