Large deviations for Wigner's law and Voiculescu's non-commutative entropy

G. Ben Arous, A. Guionnet

Research output: Contribution to journalArticlepeer-review

Abstract

We study the spectral measure of Gaussian Wigner's matrices and prove that it satisfies a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner's semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about Voiculescu's non commutative entropy.

Original languageEnglish (US)
Pages (from-to)517-542
Number of pages26
JournalProbability Theory and Related Fields
Volume108
Issue number4
DOIs
StatePublished - Aug 1997

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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