On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble

T. Shcherbina

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We consider the deformed Gaussian ensemble Hn=Hn (0) + Mn in which Hn (0) is a hermitian matrix (possibly random) and Mn is the Gaussian unitary random matrix (GUE) independent of Hn (0). Assuming that the Normalized Counting Measure of Hn (0) converges weakly (in probability if random) to a non-random measure N(0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of Hn.

Original languageEnglish (US)
Pages (from-to)455-481
Number of pages27
JournalJournal of Statistical Physics
Volume143
Issue number3
DOIs
StatePublished - May 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Airy kernel
  • Deformed GUE
  • Edge universality
  • Random matrices

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