The right tail exponent of the Tracy-Widom-beta distribution
Probability
2014-01-27 v1
Abstract
The Tracy-Widom beta distribution is the large dimensional limit of the top eigenvalue of beta random matrix ensembles. We use the stochastic Airy operator representation to show that as a tends to infinity the tail of the Tracy Widom distribution satisfies P(TW_beta > a) = a^(-3/4 beta+o(1)) exp(-2/3 beta a^(3/2)).
Keywords
Cite
@article{arxiv.1102.4818,
title = {The right tail exponent of the Tracy-Widom-beta distribution},
author = {Laure Dumaz and Bálint Virág},
journal= {arXiv preprint arXiv:1102.4818},
year = {2014}
}