A Note on the Analyticity of Density of States

TL;DR

This paper proves the local analyticity of the density of states in the Anderson model under certain conditions, using complex analysis and random walk expansions, with implications for correlation functions.

Contribution

It establishes the analyticity of the density of states for large disorder and locally analytic potentials, extending previous results with sharper bounds and broader applicability.

Findings

Density of states is locally analytic under specified conditions

Method employs random walk expansion and complex analysis techniques

Results include sharper bounds for the uniform distribution case

Abstract

We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of resolvents and a simple complex function theory trick. In particular, we discuss the uniform distribution case, and we obtain a sharper result using more precise computations. The method can be also applied to prove the analyticity of the correlation functions.