Dependence of the density of states on the probability distribution -- part II: Schr\"odinger operators on $\mathbb{R}^d$ and non-compactly supported probability measures

Abstract

We extend our results in \cite{hislop_marx_1} on the quantitative continuity properties, with respect to the single-site probability measure, of the density of states measure and the integrated density of states for random Schr\"odinger operators. For lattice models on $\mathbb{Z}^d$, with $d \geq 1$, we treat the case of non-compactly supported probability measures with finite first moments. For random Schr\"odinger operators on $\mathbb{R}^d$, with $d \geq 1$, we prove results analogous to those in \cite{hislop_marx_1} for compactly supported probability measures. The method of proof makes use of the Combes-Thomas estimate and the Helffer-Sj\"ostrand formula.