Semicircle law for a matrix ensemble with dependent entries
Mathematical Physics
2014-02-25 v3 math.MP
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. ). We also investigate the largest eigenvalue of certain ensembles of Curie-Weiss type and find a transition in its behavior at the critical temperature.
Cite
@article{arxiv.1401.6636,
title = {Semicircle law for a matrix ensemble with dependent entries},
author = {Winfried Hochstättler and Werner Kirsch and Simone Warzel},
journal= {arXiv preprint arXiv:1401.6636},
year = {2014}
}