The right tail exponent of the Tracy-Widom-beta distribution
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(TWbeta > a) = a(-3/4 beta+o(1)) exp(-2/3 beta a(3/2)).
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