Right tail expansion of Tracy-Widom beta laws

Gaëtan Borot, Céline Nadal

Published 2011-11-11Version 1

Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian beta matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic expansion of the right tail Tracy-Widom beta laws, for all positive beta, by studying the double scaling limit.