On the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians

Abstract

The aim of this work is to extend the results from Bourgain (On eigenvalue spacings for the 1D Anderson model with singular site distribution) on local eigenvalue spacings to certain 1D lattice Schrodinger with a Bernoulli potential.We assume the disorder satisfies a certain algebraic condition that enables one to invoke the recent results from Bourgain (An application of group expansion to the Anderson-Bernoulli model. Preprint) on the regularity of the density of states. In particular we establish Poisson local eigenvalue statistics in those models.