An application of group expansion to the Anderson-Bernoulli model

TL;DR

This paper proves that the density of states for certain 1D lattice Schrödinger operators with binary potential values is smooth, under specific conditions on the potential strength and energy range.

Contribution

It introduces an application of group expansion techniques to establish smoothness of the density of states in the Anderson-Bernoulli model for small algebraic potential values.

Findings

Density of states is smooth for the model.

Smoothness holds for small algebraic potential values.

Results apply away from the spectral edges.

Abstract

We establish smoothness of the density of states for 1D lattice Schrodinger operators with potential taking values $\pm\lambda$, for $\lambda$ in a class of small algebraic numbers and energy $E\in)-2, 2($ suitably restricted away from $\pm2$.