Continuity with respect to disorder of the integrated density of states

Abstract

We prove that the integrated density of states (IDS) associated to a random Schrödinger operator is locally uniformly Hölder continuous as a function of the disorder parameter $\lambda$. In particular, we obtain convergence of the IDS, as $\lambda \rightarrow 0$, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.