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 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 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 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 …

We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of
high-dimensional sample covariance matrices. To be precise, we show that the fluctuations …

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+ …

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 properties of the ground state density for the d-dimensional Fermi gas in an
harmonic trap. Previous work has shown that the d-dimensional Fourier transform has a very …

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 …

We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix H
converge to the Tracy–Widom laws at a rate nearly O (N− 1∕ 3), as the matrix dimension N …