Janossy densities for Unitary ensembles at the spectral edge

Details Janossy densities for Unitary ensembles at the spectral edge Janossy densities for Unitary ensembles at the spectral edge

2007-06-06

arxiv.org/abs/0706.0921v2

Mathematics

Probability

6 figures, corrected typos, one erroneous corollary eliminated

Scientific paper

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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