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

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 .

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 .

DOI : https://doi.org/10.1214/11-AIHP475
Classification:  60F10,  60H25
Keywords: Tracy-Widom distribution, stochastic airy operator, beta ensembles
@article{AIHPB_2013__49_4_915_0,
     author = {Dumaz, Laure and Vir\'ag, B\'alint},
     title = {The right tail exponent of the Tracy-Widom $\beta $ distribution},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {4},
     year = {2013},
     pages = {915-933},
     doi = {10.1214/11-AIHP475},
     zbl = {1278.60012},
     mrnumber = {3127907},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2013__49_4_915_0}
}
The right tail exponent of the Tracy-Widom $\beta $ distribution. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 4, pp. 915-933. doi : 10.1214/11-AIHP475. http://www.numdam.org/item/AIHPB_2013__49_4_915_0/

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