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

I. V. Krasovsky
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Abstract

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.

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I. V. Krasovsky. 2007-06-21. Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant. https://arxiv.org/abs/math-ph/0411016

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