We consider the real eigenvalues of the elliptic Ginibre matrix indexed by the non-Hermiticity
parameter τ∈[0, 1], and present a Harer-Zagier type recursion formula for the even moments …

The moments of the real eigenvalues of real Ginibre matrices are investigated from the
viewpoint of explicit formulas, differential and difference equations, and large N expansions …

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 …

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 consider some discrete $ q $-analogues of the classical continuous orthogonal
polynomial ensembles. Building on results due to Morozov, Popolitov and Shakirov, we find …

The eigenvalue probability density function of the Gaussian unitary ensemble permits a $ q
$-extension related to the discrete $ q $-Hermite weight and corresponding $ q $-orthogonal …

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 …