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Title:聽Sharp tail estimates in beta ensembles.

Abstract:聽Hermite and Laguerre beta ensembles are well studied models in random matrix theory with the special cases beta=1,2,4 corresponding to classical Gaussian and Wishart random matrices. Using tridiagonal matrix models for these ensembles, Ramirez, Rider and Virag established Tracy-Widom beta scaling limits for the largest eigenvalues. They also showed upper and lower tail decay rate for these distributions. I shall present the work establishing sharp tail estimates in the pre-limiting models up to 1+o(1) error at the level of exponents, improving earlier results of Ledoux and Rider. This talk is based on a joint work with Basu, Bhattacharjee and Krishnapur.

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