Covariances and variances of linear statistics of a point process can be written as integrals
over the truncated two-point correlation function. When the point process consists of the …

We obtain large n asymptotics of n× n Hankel determinants whose weight has a one-cut
regular potential and Fisher-Hartwig singularities. We restrict our attention to the case where …

In the classical β-ensembles of random matrix theory, setting β= 2α/N and taking the N→∞
limit gives a statistical state depending on α. Using the loop equations for the classical β …

We establish a new connection between moments of n * nn× n random matrices X n and
hypergeometric orthogonal polynomials. Specifically, we consider moments E\rm Tr X_n^-s …

We consider the Laguerre partition function and derive explicit generating functions for
connected correlators with arbitrary integer powers of traces in terms of products of Hahn …

Integer moments of complex Wishart matrices and Hurwitz numbers Page 1 Ann. Inst. Henri
Poincaré Comb. Phys. Interact. 8 (2021), 243–268 DOI 10.4171/AIHPD/103 Integer …

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 …

Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and
Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The …

Representation theory and the theory of symmetric functions have played a central role in
random matrix theory in the computation of quantities such as joint moments of traces and …

In recent work, the authors have shown that the eigenvalue probability density function for
Dyson Brownian motion from the identity on U (N) is an example of a newly identified class …