Regularity of the density of states for random Dirac operators

TL;DR

This paper proves Lipschitz regularity of the density of states for random Dirac operators using a novel approach based on the Helffer-Sj"ostrand formula, building on previous localization results.

Contribution

It introduces a new method for establishing regularity of the density of states in random Dirac operators, distinct from traditional Schr"odinger operator techniques.

Findings

Proved Lipschitz regularity of the density of states.

Developed a new approach using the Helffer-Sj"ostrand formula.

Built upon previous localization results for random Dirac operators.

Abstract

We consider the random Dirac operators for which we have proved Anderson localization in arXiv:1812.01868. We use the Wegner estimate we have got in that paper to prove Lipschitz regularity of the density of states. Since usual methods for Schr\"odinger operators do not work in this case, we give a new one based on the Helffer-Sj\"ostrand formula.