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

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

2011-02-23

arxiv.org/abs/1102.4818v1

Mathematics

Probability

Scientific paper

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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