Large deviation eigenvalue density for the soft edge Laguerre and Jacobi $\beta$-ensembles

Abstract

We analyze the eigenvalue density for the Laguerre and Jacobi $\beta$-ensembles in the cases that the corresponding exponents are extensive. In particular, we obtain the asymptotic expansion up to terms $o(1)$, in the large deviation regime outside the limiting interval of support. As found in recent studies of the large deviation density for the Gaussian $\beta$-ensemble, and Laguerre $\beta$-ensemble with fixed exponent, there is a scaling from this asymptotic expansion to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge.

18 pages

References in corpus (7)

• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy--Widom limits and rates of convergence
• Moments of the transmission eigenvalues, proper delay times and random matrix theory II
• Right tail expansion of Tracy-Widom beta laws
• Asymptotic forms for hard and soft edge general $\beta$ conditional gap probabilities
• Asymptotics of Selberg-like integrals by lattice path counting

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