Publications [#244287] of Xin Zhou

Papers Published

1. Rider, B; Zhou, X, Janossy densities for unitary ensembles at the spectral edge, International Mathematics Research Notices, vol. 2008 no. 1 (December, 2008), Oxford University Press (OUP), ISSN 1073-7928 [doi]
   (last updated on 2024/04/24)

   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. © The Author 2008. Published by Oxford University Press. All rights reserved.