Wegner estimate for discrete Schr\"odinger operators with Gaussian random potentials

TL;DR

This paper establishes a Wegner estimate for discrete Schr"odinger operators with Gaussian potentials, requiring only exponential decay of the covariance, thus broadening applicability beyond previous models.

Contribution

It provides the first Wegner estimate for Gaussian potentials with minimal assumptions on covariance decay, removing the need for monotonicity or positivity conditions.

Findings

Wegner estimate proven for Gaussian potentials with exponential covariance decay

No monotonicity or positivity assumptions needed

Results extend the class of models with proven localization properties

Abstract

We prove a Wegner estimate for discrete Schr\"odinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially, no monotonicity assumption is required. This improves earlier results where abstract conditions on the conditional distribution, compactly supported and non-negative, or compactly supported covariance functions with positive mean are considered.