Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant

I. V. Krasovsky

Published 2004-11-04, updated 2007-06-21Version 4

We obtain large n asymptotics for products of powers of the absolute values of the characteristic polynomials in the Gaussian Unitary Ensemble of n\times n matrices. Our results can also be interpreted as asymptotics of the determinant of a Hankel matrix whose symbol is supported on the real line and possesses power-like (Fisher-Hartwig) singularities.