Right tail expansion of Tracy-Widom beta laws

Abstract

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.

23 pages

References in corpus (2)

• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function

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