Universality of local eigenvalue statistics for some sample covariance matrices

G. Ben Arous, S. Péché

Research output: Contribution to journalArticlepeer-review


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
Issue number10
StatePublished - Oct 2005

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Universality of local eigenvalue statistics for some sample covariance matrices'. Together they form a unique fingerprint.

Cite this