Igor Krasovsky (Imperial College)

Strong and weak confinement in the Freud ensemble of random matrices

Abstract:

We discuss the Freud ensemble of random matrices (the unitary ensemble associated with the Freud orthogonal polynomials with weight exp(-|x|^β), β>0). At the point x=0, a curious transition takes place when β 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 β<1 and β>1. This is a joint work with Tom Claeys and Olexander Minakov.