Journal article

Asymptotic correlations for Gaussian and Wishart matrices with external source

Patrick Desrosiers, Peter J Forrester

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | OXFORD UNIV PRESS | Published : 2006

Abstract

We consider ensembles of Gaussian (Hermite) and Wishart (Laguerre) N×N Hermitian matrices. We study the effect of finite-rank perturbations of these ensembles by a source term. The rank r of the perturbation corresponds to the number of nonnull eigenvalues of the source matrix. In the perturbed ensembles, the correlation functions can be written in terms of kernels. We show that for all N, the difference between the perturbed and the unperturbed kernels is a degenerate kernel of size r which depends on multiple Hermite or Laguerre functions.We also compute asymptotic formulas for the multiple Laguerre functions kernels in terms of multiple Bessel (resp., Airy) functions. This leads to the la..

View full abstract

University of Melbourne Researchers