Existence of the density of states for some alloy type models with single site potentials of changing sign

TL;DR

This paper proves the existence of the density of states for certain alloy-type random Schrödinger operators with sign-changing potentials and discusses implications for Anderson localization.

Contribution

It establishes the existence of the density of states for alloy models with sign-changing potentials and derives a Wegner estimate implying localization.

Findings

Density of states exists for specified alloy models.

Wegner estimate obtained under certain conditions.

Implications for Anderson localization in these models.

Abstract

We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate we prove implies Anderson localization under certain additional assumptions. For some examples we discuss briefly some properties of the common and conditional densities of the random coupling constants used in the proof of the Wegner estimate.