%0 Journal Article
%T Janossy densities for Unitary ensembles at the spectral edge
%A Brian Rider
%A Xin Zhou
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0706.0921v2