Wegner estimate and the density of states of some indefinite alloy type Schroedinger Operators

TL;DR

This paper establishes a Wegner estimate for certain indefinite alloy-type Schrödinger operators, which is crucial for proving pure point spectrum and the existence of the density of states across all energies and dimensions.

Contribution

It introduces a Wegner estimate applicable to Schrödinger operators with sign-changing potentials, advancing understanding of their spectral properties.

Findings

Proves Wegner estimate for indefinite alloy potentials

Establishes existence of density of states for these operators

Demonstrates pure point spectrum in the studied class

Abstract

We study Schroedinger operators with a random potential of alloy type. The single site potentials are allowed to change sign. For a certain class of them we prove a Wegner estimate. This is a key ingredient in an existence proof of pure point spectrum of the considered random Schroedinger operators. Our estimate is valid for all bounded energy intervals and all space dimensions and implies the existence of the density of states.