Semicircle Law for a Matrix Ensemble with Dependent Entries

Winfried Hochstättler, Werner Kirsch, Simone Warzel

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie–Weiss type. We provide a criterion on the correlations ensuring the validity of Wigner’s semicircle law for the eigenvalue distribution measure. In case of Curie–Weiss distributions, this criterion applies above the critical temperature (i.e., β<1). We also investigate the largest eigenvalue of certain ensembles of Curie–Weiss type and find a transition in its behavior at the critical temperature.

Original languageEnglish
Pages (from-to)1047-1068
Number of pages22
JournalJournal of Theoretical Probability
Volume29
Issue number3
DOIs
StatePublished - 1 Sep 2016

Keywords

  • Curie–Weiss model
  • Random matrices
  • Semicircle law

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