Hölder equicontinuity of the integrated density of states at weak disorder

Abstract

Hölder continuity, $|N_{\lambda }(E)-N_{\lambda }(E^{\prime })|\le C|E-E^{\prime }{|}^{\alpha }$, with a constant $C$ independent of the disorder strength $\lambda$ is proved for the integrated density of states $N_{\lambda }(E)$ associated to a discrete random operator $H=H_o+\lambda V$ 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.

15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combined