Eigenvalue Statistics for Random Schrödinger Operators with Non Rank One Perturbations

Peter D. Hislop, M. Krishna

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We prove that certain natural random variables associated with the local eigenvalue statistics for generalized lattice Anderson models constructed with finite-rank perturbations are compound Poisson distributed. This distribution is characterized by the fact that the Lévy measure is supported on at most a finite set of positive integers determined by the rank. The proof relies on a Minami-type estimate for finite-rank perturbations. For Anderson-type continuum models on $${{\mathbb{R}^d}}$$Rd, we prove a similar result for certain natural random variables associated with the local eigenvalue statistics. We prove that the compound Poisson distribution associated with these random variables has a Lévy measure whose support is at most the set of positive integers.

Original languageEnglish
Pages (from-to)125-143
Number of pages19
JournalCommunications in Mathematical Physics
Volume340
Issue number1
DOIs
StatePublished - Nov 14 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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