Universality of local eigenvalue statistics for some sample covariance matrices

G. Ben Arous, S. Péché

Research output: Contribution to journalArticle

Abstract

We consider random, complex sample covariance matrices 1/N X*X, where X is a p × N random matrix with i.i.d. entries of distribution μ. It has been conjectured that both the distribution of the distance between nearest neighbor eigenvalues in the bulk and that of the smallest eigenvalues become, in the limit N → ∞, p/N → 1, the same as that identified for a complex Gaussian distribution μ. We prove these conjectures for a certain class of probability distributions μ.

Original languageEnglish (US)
Pages (from-to)1316-1357
Number of pages42
JournalCommunications on Pure and Applied Mathematics
Volume58
Issue number10
DOIs
StatePublished - Oct 2005

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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