Igor Krasovsky: Strong and weak confinement in the Freud ensemble of random matrices

Date: 2024-10-10

Time: 14:00 - 15:00

Speaker

Igor Krasovsky, Imperial College London

Abstract

We discuss the Freud ensemble of random matrices (the unitary ensemble associated with the Freud orthogonal polynomials with weight exp(-|x|^beta), beta>0).

At the point x=0, a curious transition takes place when beta crosses the value 1. We obtain asymptotic formulas for the probability of a large gap around x=0 in the local scaling regime and present the 2 distinct cases for beta<1 and beta>1. This is a joint work with Tom Claeys and Olexander Minakov.