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

Peter D. Hislop, Christoph A. Marx

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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 Zd, with d⩾ 1 , we treat the case of non-compactly supported probability measures with finite first moments. For random Schrödinger operators on Rd, 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.

Original languageEnglish
Pages (from-to)539-570
Number of pages32
JournalAnnales Henri Poincare
Volume21
Issue number2
DOIs
StatePublished - Feb 1 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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