Dependence of the density of states on the probability distribution -- part II: Schrödinger 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 Schrödinger operators. For lattice models on ${\mathbb{Z}}^d$, with $d\ge 1$, we treat the case of non-compactly supported probability measures with finite first moments. For random Schrödinger operators on ${\mathbb{R}}^d$, with $d\ge 1$, 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-Sjöstrand formula.

28 pages; typos corrected; proof of Proposition 2.2 rewritten and improved; section 3.2 rewritten and Proposition 3.2 improved to Lipschitz continuity for all dimensions; all main results in version 1 remain the same

References in corpus (2)

• Bounds on the density of states for Schr\" odinger operators
• An Improved Combes-Thomas Estimate of Magnetic Schrödinger Operators