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

I. V. Krasovsky

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

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arxiv math-ph/0411016 v4 pith:T7YP2HJH submitted 2004-11-04 math-ph math.MP

I. V. Krasovsky This is my paper · ORCID

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keywords asymptoticscharacteristicdeterminantensemblegaussianhankelpolynomialsunitary

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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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A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants
math-ph 2019-09 accept novelty 8.0 of 10

A 4x4 Riemann-Hilbert formalism gives large-n asymptotics for Toeplitz+Hankel determinants with independent symbols, conditional on a non-degeneracy bound and verified for an explicit family.

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