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arXiv · 1201.3055

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

Peter J. Forrester
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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.

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Peter J. Forrester. 2012-01-15. Large deviation eigenvalue density for the soft edge Laguerre and Jacobi $\beta$-ensembles. https://doi.org/10.1088/1751-8113/45/14/145201

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