Bulk Universality of General $\beta$-Ensembles with Non-convex Potential
Probability
2015-06-03 v2 Mathematical Physics
math.MP
Abstract
We prove the bulk universality of the -ensembles with non-convex regular analytic potentials for any . This removes the convexity assumption appeared in our earlier work. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification.
Keywords
Cite
@article{arxiv.1201.2283,
title = {Bulk Universality of General $\beta$-Ensembles with Non-convex Potential},
author = {Paul Bourgade and Laszlo Erdos and Horng-Tzer Yau},
journal= {arXiv preprint arXiv:1201.2283},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1104.2272