Title: Universal behavior for averages of characteristic polynomials at the origin of the spectrum
Authors: Vanlessen, Maarten # ×
Issue Date: 2005
Publisher: Springer
Series Title: Communications in mathematical physics vol:253 issue:3 pages:535-560
Abstract: It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy transforms. We will show that, for the unitary ensemble 1/Z(n) \det M\(2alpha)e(-nV(M))dM of n x n Hermitian matrices, these kernels have universal behavior at the origin of the spectrum, as n --> infinity, in terms of Bessel functions. Our approach is based on the characterization of orthogonal polynomials together with their Cauchy transforms via a matrix Riemann-Hilbert problem, due to Fokas, Its and Kitaev, and on an application of the Deift/Zhou steepest descent method for matrix Riemann-Hilbert problems to obtain the asymptotic behavior of the Riemann-Hilbert problem.
ISSN: 0010-3616
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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