The right tail exponent of the Tracy-Widom β distribution
Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 4, pp. 915-933.

La loi de Tracy-Widom β est la limite de la plus grande valeur propre des ensembles β de matrices aléatoires lorsque leur taille tend vers l’infini. Nous utilisons la représentation par l’opérateur stochastique d’Airy pour montrer que lorsque a→∞ la queue de la loi de Tracy-Widom vérifie :

P(𝑇𝑊 β >a)=a -(3/4)β+o(1) exp- 2 3 β a 3/2 .

The Tracy-Widom β distribution is the large dimensional limit of the top eigenvalue of β random matrix ensembles. We use the stochastic Airy operator representation to show that as a→∞ the tail of the Tracy-Widom distribution satisfies

P(𝑇𝑊 β >a)=a -(3/4)β+o(1) exp- 2 3 β a 3/2 .

DOI : 10.1214/11-AIHP475
Classification : 60F10, 60H25
Mots-clés : Tracy-Widom distribution, stochastic airy operator, beta ensembles 
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Dumaz, Laure; Virág, Bálint. The right tail exponent of the Tracy-Widom $\beta $ distribution. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 4, pp. 915-933. doi : 10.1214/11-AIHP475. http://archive.numdam.org/articles/10.1214/11-AIHP475/

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