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 language | English |
---|---|
Pages (from-to) | 1047-1068 |
Number of pages | 22 |
Journal | Journal of Theoretical Probability |
Volume | 29 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2016 |
Keywords
- Curie–Weiss model
- Random matrices
- Semicircle law