The right tail exponent of the Tracy-Widom-beta distribution

Abstract

The Tracy-Widom beta distribution is the large dimensional limit of the top eigenvalue of beta random matrix ensembles. We use the stochastic Airy operator representation to show that as a tends to infinity the tail of the Tracy Widom distribution satisfies P(TW_beta > a) = a^(-3/4 beta+o(1)) exp(-2/3 beta a^(3/2)).

References in corpus (4)

• Beta ensembles, stochastic Airy spectrum, and a diffusion
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Large deviations of the maximal eigenvalue of random matrices
• Large gaps between random eigenvalues

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• Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices
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• Tracy-Widom at high temperature
• Linear Differential Equations for the Resolvents of the Classical Matrix Ensembles
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• At the edge of a one-dimensional jellium
• The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem
• Random matrices in non-confining potentials
• Optimal tail estimates in $\beta$-ensembles and applications to last passage percolation
• Computing the Tracy-Widom Distribution for Arbitrary $\beta >0$
• The Tracy-Widom distribution at large Dyson index