Lipschitz-continuity of the integrated density of states for Gaussian random potentials

TL;DR

This paper proves that the integrated density of states for a Schrödinger operator with a Gaussian random potential is locally Lipschitz-continuous, using a Wegner estimate, under specific conditions on the covariance function.

Contribution

It establishes the Lipschitz continuity of the integrated density of states for Gaussian random potentials with certain covariance properties, a result not previously shown.

Findings

Integrated density of states is locally Lipschitz-continuous.

Lipschitz continuity is proven using a Wegner estimate.

Results apply to Gaussian potentials with continuous, compactly supported covariance.

Abstract

The integrated density of states of a Schroedinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive mean, is locally uniformly Lipschitz-continuous. This is proven using a Wegner estimate.