Level density for deformations of the Gaussian orthogonal ensemble.

Abstract

Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles, we derive formulas for the average level density for sid the transition from the Gaussian orthogonal ensemble sGOEd to the Poisson ensemble and siid the transition from the GOE to m GOEs.