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arXiv · 1102.4818

The right tail exponent of the Tracy-Widom-beta distribution

Laure Dumaz·Bálint Virág
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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)).

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Laure Dumaz, Bálint Virág. 2011-02-23. The right tail exponent of the Tracy-Widom-beta distribution. https://doi.org/10.1214/11-aihp475

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