Dependence of the Density of States on the Probability Distribution. Part II: Schrödinger Operators on R^d and Non-compactly Supported Probability Measures

We extend our results in Hislop and Marx (Int Math Res Not, 2018. https://doi.org/10.1093/imrn/rny156) 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 Z^d, with d⩾ 1 , we treat the case of non-compactly supported probability measures with finite first moments. For random Schrödinger operators on R^d, with d⩾ 1 , we prove results analogous to those in Hislop and Marx (2018) for compactly supported probability measures. The method of proof makes use of the Combes–Thomas estimate and the Helffer–Sjöstrand formula.