On universality of bulk local regime of the deformed Gaussian unitary ensemble

T. Shcherbina

Research output: Contribution to journalArticle

17 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 Ensemble (GUE) random matrix (independent of Hn(0)). Assuming that the Normalized Counting Measure of Hn(0) converges weakly (in probability) to a nonrandom measure N (0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.

Original languageEnglish (US)
Pages (from-to)396-433
Number of pages38
JournalJournal of Mathematical Physics, Analysis, Geometry
Volume5
Issue number4
StatePublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Keywords

  • Gaussian unitary ensemble
  • Random matrices
  • Universality

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