Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant

Igor Krasovsky

Type: Article

Publication Date: 2007-09-15

Citations: 75

DOI: https://doi.org/10.1215/s0012-7094-07-13936-x

Abstract

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

Locations

Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF

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