2007/06/06 by Brian Rider, Xin Zhou, Rider, Brian +1
Mathematics · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.0706.0921
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.