Alisa Knizel: Discrete beta-corners processes and loop equations

Abstract

I will talk about joint work with E. Dimitrov on discrete log-gases. We introduce and study global asymptotics of linear statistics for a class of discrete particle ensembles that naturally arise in connection with classical random matrix ensembles and Jack polynomials. Our main tools are certain novel algebraic identities that play a role of discrete multi-level analogues of loop equations.