Universality of General $\beta$-Ensembles
Probability
2015-01-14 v5 Mathematical Physics
math.MP
Abstract
We prove the universality of the -ensembles with convex analytic potentials and for any , i.e. we show that the spacing distributions of log-gases at any inverse temperature coincide with those of the Gaussian -ensembles.
Cite
@article{arxiv.1104.2272,
title = {Universality of General $\beta$-Ensembles},
author = {Paul Bourgade and Laszlo Erdos and Horng-Tzer Yau},
journal= {arXiv preprint arXiv:1104.2272},
year = {2015}
}
Comments
Sep 21, 2011: Lemma 3.9 was corrected. Feb 5: Some typos in Lemma 5.9 were corrected