The right tail exponent of the Tracy–Widom $\beta$ distribution

Laure Dumaz (1, 2) , Bálint Virág

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LMO - Laboratoire de Mathématiques d'Orsay

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)).

Domaines: Mathématiques [math]

Laure Dumaz, Bálint Virág. The right tail exponent of the Tracy–Widom $\beta$ distribution. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2013, 49 (4), pp.915-933. ⟨10.1214/11-AIHP475⟩. ⟨hal-03013443⟩