Janossy densities for unitary ensembles at the spectral edge

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Rider, B; Zhou, X

Published Date

  • December 1, 2008

Published In

Volume / Issue

  • 2008 / 1

Electronic International Standard Serial Number (EISSN)

  • 1687-0247

International Standard Serial Number (ISSN)

  • 1073-7928

Digital Object Identifier (DOI)

  • 10.1093/imrn/rnn037

Citation Source

  • Scopus