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 on the band/system size. We analyse the implications of this distribution to the inverse participation ratio, level spacing statistics and the problem of two interacting particles in a random potential.