Correlations of the characteristic polynomials in the gaussian unitary ensemble or a singular hankel determinant

摘要

We obtain large it asymptotics for products of powers of the absolute values of the characteristic polynomials in the Gaussian unitary ensemble (GUE) of (n x 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.