On universality of bulk local regime of the Hermitian sample covariance matrices

Tatyana Shcherbina

Research output: Contribution to journalArticle

Abstract

We consider the Hermitian sample covariance matrices Hn=m-1Σn1/2Am,nAm,n*Σn1/2 in which Σn is a positive definite Hermitian matrix (possibly random) and Am,n is a n×m complex Gaussian random matrix (independent of Σn), and m→∞, n→∞, such that mn-1→c>1. Assuming that the normalized counting measure of Σn 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)
Article number103516
JournalJournal of Mathematical Physics
Volume51
Issue number10
DOIs
StatePublished - Oct 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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