Local eigenvalue statistics for higher-rank Anderson models after Dietlein-Elgart

Samuel Herschenfeld, Peter D. Hislop

Research output: Contribution to journalArticlepeer-review


We use the method of eigenvalue level spacing developed by Dietlein and Elgart [Level spacing and Poisson statistics for continuum random Schrodinger operators, J. Eur. Math. Soc. (JEMS) 23(4) (2021) 1257-1293] to prove that the local eigenvalue statistics (LES) for the Anderson model on d, with uniform higher-rank 2, single-site perturbations, is given by a Poisson point process with intensity measure n(E0)ds, where n(E0) is the density of states at energy E0 in the region of localization near the spectral band edges. This improves the result of Hislop and Krishna [Eigenvalue statistics for random Schrodinger operators with non-rank one perturbations, Comm. Math. Phys. 340(1) (2015) 125-143], who proved that the LES is a compound Poisson process with Levy measure supported on the set {1, 2,m}. Our proofs are an application of the ideas of Dietlein and Elgart to these higher-rank lattice models with two spectral band edges, and illustrate, in a simpler setting, the key steps of the proof of Dietlein and Elgart.

Original languageEnglish
Article number2350017
JournalReviews in Mathematical Physics
Issue number8
StatePublished - Sep 1 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.


  • Minami estimate
  • Random Schrödinger operators
  • eigenvalue statistics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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