Eigenvalue statistics of distorted random matrices

Abstract

A numerical study of a set of random matrices which interpolate Poisson and Gaussian orthogonal ensembles is reported. The result indicates that the transition from Poisson to Wigner distributions for the nearest-level spacing does not depend on the details of the random-matrix parametrization and is essentially governed by a single parameter. Brody's one-parameter interpolation formula is found to describe the transition rather well.