The right tail exponent of the Tracy-Widom β distribution
Dumaz, Laure ; Virág, Bálint
Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013), p. 915-933 / Harvested from Numdam
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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 .

Publié le : 2013-01-01
DOI : https://doi.org/10.1214/11-AIHP475
Classification:  60F10,  60H25 
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     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},
     volume = {49},
     year = {2013},
     pages = {915-933},
     doi = {10.1214/11-AIHP475},
     mrnumber = {3127907},
     zbl = {1278.60012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2013__49_4_915_0}
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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) pp. 915-933. doi : 10.1214/11-AIHP475. http://gdmltest.u-ga.fr/item/AIHPB_2013__49_4_915_0/

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