On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials

TL;DR

This paper investigates the spectral properties of random Schrödinger operators with sign-changing potentials, establishing a Wegner estimate and proving Lipschitz continuity of the integrated density of states in certain regimes.

Contribution

It introduces a finite section method for Toeplitz matrices to handle sign-indefinite potentials, extending spectral analysis techniques to new alloy-type models.

Findings

Proved a Wegner estimate for sign-changing potentials.

Established Lipschitz continuity of the integrated density of states.

Demonstrated localization near spectral edges in specific disorder regimes.

Abstract

The present paper is devoted to the study of spectral properties of random Schroedinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is allowed to change sign. The results apply to the corresponding discrete model, too. In certain disorder regimes we are able to prove the Lipschitz continuity of the integrated density of states and/or localization near spectral edges.