Regularity of the density of states for random Dirac operators

Abstract

We consider random Dirac operators for which we have proved Anderson localization in the work of J.-M. Barbaroux, H. D. Cornean, and S. Zalczer [“Localization for gapped Dirac Hamiltonians with random perturbations: Application to graphene antidot lattices,” Doc. Math. 24, 65–93 (2019)]. We use the Wegner estimate we have got in that paper to prove Lipschitz regularity of the density of states. We use a method based on the Helffer–Sjöstrand formula to get information on the density of states from the Wegner estimate we have proven in the first article.