A simple extension of Stollmann's lemma to correlated potentials

TL;DR

This paper extends Stollmann's lemma to correlated potentials, enabling Wegner-type estimates in spectral analysis of complex random operators like multi-particle Hamiltonians.

Contribution

It introduces a natural extension of Stollmann's lemma to correlated variables, broadening its applicability in spectral analysis.

Findings

Enables Wegner-type estimates for correlated potentials

Applicable to multi-particle Hamiltonians

Simplifies analysis of spectral properties in complex systems

Abstract

We propose a fairly simple and natural extension of Stollmann's lemma to correlated random variables. This extension allows (just as the original Stollmann's lemma does) to obtain Wegner-type estimates even in some problems of spectral analysis of random operators where the Wegner's lemma is inapplicable (e.g. for multi-particle Hamiltonians).