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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}
}