Optimal volume Wegner estimate for random magnetic Laplacians on ${\mathbb {Z}}^2$Z2

Abstract

We consider a two dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove a Wegner estimate with optimal volume dependence. The Wegner estimate holds around the spectral edges, and it implies Hölder continuity of the integrated density of states in this region. The proof is based on the Wegner estimate obtained in Erdős and Hasler [“Wegner estimate for random magnetic Laplacians on ${\mathbb {Z}}^2$Z2,” Ann. Henri Poincaré 12, 1719–1731 (2012)]10.1007/s00023-012-0177-9.