Hidden Breit-Wigner Distribution and Other Properties of Random Matrices with Preferential Basis

Abstract

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized regimes with width independent of the band or system size. We analyze the implications of this distribution to the inverse participation ratio, level spacing statistics, and the problem of two interacting particles in a random potential.