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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have