A lower bound for the density of states of the lattice Anderson model

Peter D. Hislop, Peter Müller

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and the probability measure has a bounded Lebesgue density with compact support, and if this density is essentially bounded away from zero on its support, then we prove that the density of states is strictly positive for Lebesgue-almost every energy in the deterministic spectrum.

Original languageEnglish
Pages (from-to)2887-2893
Number of pages7
JournalProceedings of the American Mathematical Society
Volume136
Issue number8
DOIs
StatePublished - Aug 2008

Keywords

  • Integrated density of states
  • Lower bound
  • Random Schrödinger operators
  • Wegner estimate

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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