H\"older equicontinuity of the integrated density of states at weak disorder

TL;DR

This paper proves that the integrated density of states for a class of random operators exhibits H"older continuity with a disorder-independent constant, under certain regularity conditions.

Contribution

It establishes disorder-independent H"older continuity of the integrated density of states for discrete random operators with absolutely continuous potentials.

Findings

H"older continuity of $N_mbda(E)$ with exponent $lpha$

Constant $C$ is independent of disorder strength $mbda$

Results hold under regularity assumptions for the hopping term

Abstract

H\"older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, 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.