The goal of this article is to study how much the eigenvalues of large Hermitian random
matrices deviate from certain deterministic locations—or in other words, to investigate …

We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m
of discontinuities. These m-point determinants are generating functions for the Airy point …

Universality of eigenvalue spacings is one of the basic characteristics of random matrices.
We give the precise meaning of universality and discuss the standard universality classes …

We consider the determinantal point process with the confluent hypergeometric kernel. This
process is a universal point process in random matrix theory and describes the distribution …

We obtain exponential moment asymptotics for the Bessel point process. As a direct
consequence, we improve on the asymptotics for the expectation and variance of the …

We consider the generating function of the sine point process on m consecutive intervals. It
can be written as a Fredholm determinant with discontinuities, or equivalently as the …

We describe an approach to universality limits for orthogonal polynomials on the real line
which is completely local and uses only the boundary behavior of the Weyl m-function at the …

In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth
Jacobi-type densities are considered. It is assumed that densities are supported on mutually …

We find and discuss asymptotic formulas for orthonormal polynomials P n (z) with recurrence
coefficients an, bn. Our main goal is to consider the case where off-diagonal elements …

We derive necessary and sufficient conditions for universality limits for orthogonal
polynomials on the real line and related systems. One of our results is that the Christoffel …