Hölder equicontinuity of the integrated density of states at weak disorder

Abstract

Hölder continuity, $|N_λ(E)-N_λ(E')|\le C |E-E'|^α$, with a constant $C$ independent of the disorder strength $λ$ is proved for the integrated density of states $N_λ(E)$ associated to a discrete random operator $H = H_o + λV$ consisting of a translation invariant hopping matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely continuous distribution, under a regularity assumption for the hopping term.