On the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians

TL;DR

This paper extends results on local eigenvalue spacings to certain 1D Anderson-Bernoulli Hamiltonians, establishing Poisson statistics under algebraic disorder conditions, leveraging recent density of states regularity results.

Contribution

It introduces new conditions under which Poisson eigenvalue statistics hold for 1D Anderson-Bernoulli models, extending previous work.

Findings

Proves Poisson eigenvalue statistics for specific 1D models.

Identifies algebraic conditions enabling the application of recent density of states results.

Extends prior eigenvalue spacing results to Bernoulli potentials.

Abstract

The aim of this work is to extend the results from [B2] 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 [B1] on the regularity of the density of states. In particular we establish Poisson local eigenvalue statistics in those models