Correlation estimates in the anderson model

Jean V. Bellissard, Peter D. Hislop, Günter Stolz

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schrödinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment bound to obtain a new n-level Wegner-type estimate that measures eigenvalue correlations through an upper bound on the probability that a local Hamiltonian has at least n eigenvalues in a given energy interval. Another consequence of the correlation estimates is that the results on the Poisson statistics of energy level spacing and the simplicity of the eigenvalues in the strong localization regime hold for a wide class of translation-invariant, selfadjoint, lattice operators with decaying off-diagonal terms and random potentials.

Original languageEnglish
Pages (from-to)649-662
Number of pages14
JournalJournal of Statistical Physics
Volume129
Issue number4
DOIs
StatePublished - Nov 2007

Bibliographical note

Funding Information:
Authors supported in part by NSF grants DMS 06009565 (J.V.B.), 0503784 (P.D.H.), and 0245210 (G.S.).

Keywords

  • Eigenvalue statistics
  • Random operators
  • Wegner estimate

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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