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arXiv · 0706.0921

Janossy densities for Unitary ensembles at the spectral edge

Brian Rider·Xin Zhou
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Abstract

For a broad class of unitary ensembles of random matrices we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting second, third, etc. largest eigenvalues of the ensembles in question. The approach is based on a representation of the Janossy densities in terms of a system of orthogonal polynomials, plus the steepest descent method of Deift and Zhou for the asymptotic analysis of the associated Riemann-Hilbert problem.

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Brian Rider, Xin Zhou. 2008-04-08. Janossy densities for Unitary ensembles at the spectral edge. https://arxiv.org/abs/0706.0921

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