H\"older continuity of the integrated density of states in the one-dimensional Anderson model

TL;DR

This paper proves that the integrated density of states (IDS) for a one-dimensional Anderson model is Hölder continuous with an exponent depending on disorder strength, improving previous results especially for Bernoulli potentials.

Contribution

It establishes a Hölder continuity result for the IDS in the 1D Anderson model with bounded potential, extending prior work by Bourgain.

Findings

IDS is Hölder continuous with exponent 1 - c sigma

Improves the understanding of regularity of IDS in disordered systems

Extends results to more general potential distributions

Abstract

We consider the one-dimensional random Schrodinger operator H = H_0 + sigma V, where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Holder continuous with exponent 1-c sigma This improves upon the work of Bourgain showing that the Holder exponent tends to 1 as sigma tends to 0 in the more specific Anderson-Bernoulli setting.