** 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.