Universality of the Local Regime for the Block Band Matrices with a Finite Number of Blocks

Tatyana Shcherbina

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

We consider the block band matrices, i.e. the Hermitian matrices HN,N={pipe}Λ{pipe}W with elements Hjk,αβ where j,k ∈ Λ =[1,m]d ∩ ℤd (they parameterize the lattice sites) and α β = 1,...., W(they parameterize the orbitals on each site). The entries Hjk,α β are random Gaussian variables with mean zero such that 〈 Hj1k1,α1β1,Hj2k2,α2β2〉 =δj1k2δj2k1δα1β2δβ1α2Jj1k1 where J=1/W+α Δ /W, α < 1/4d. This matrices are the special case of Wegner's W-orbital models. Assuming that the number of sites {pipe}Λ{pipe} is finite, we prove universality of the local eigenvalue statistics of HN for the energies {pipe}λ0{pipe}< √2.

Original languageEnglish (US)
Pages (from-to)466-499
Number of pages34
JournalJournal of Statistical Physics
Volume155
Issue number3
DOIs
StatePublished - May 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Band matrices
  • Random matrices
  • Universality
  • Wegner model

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