The structure function of a random matrix ensemble can be specified in terms of the
covariance of the linear statistics∑ j= 1 N eik 1 λ j,∑ j= 1 N e-ik 2 λ j for Hermitian matrices …

The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix
theory, and the marginal eigenvalue distributions are basic observable quantities …

The problem of calculating the scaled limit of the joint moments of the characteristic
polynomial, and the derivative of the characteristic polynomial, for matrices from the unitary …

In this paper, we consider the elliptic Ginibre matrices in the orthogonal symmetry class that
interpolates between the real Ginibre ensemble and the Gaussian orthogonal ensemble. We …

We outline a relation between the densities for the β-ensembles with respect to the Jacobi
weight (1− x) a (1+ x) b supported on the interval (− 1, 1) and the Cauchy weight (1− ix) η (1+ …

Considered are the large N, or large intensity, forms of the distribution of the length of the
longest increasing subsequences for various models. Earlier work has established that for …

The gamma difference distribution is defined as the difference of two independent gamma
distributions, with in general different shape and rate parameters. Starting with knowledge of …

The family of circular Jacobi β ensembles has a singularity of a type associated with Fisher
and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of …

We prove an operator level limit for the circular Jacobi β-ensemble. As a result, we
characterize the counting function of the limit point process via coupled systems of stochastic …

A framework to study the eigenvalue probability density function for products of unitary
random matrices with an invariance property is developed. This involves isolating a class of …