Duke Mathematical Journal

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 (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

Article information

Source
Duke Math. J., Volume 139, Number 3 (2007), 581-619.

Dates
First available in Project Euclid: 24 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1187916271

Digital Object Identifier
doi:10.1215/S0012-7094-07-13936-X

Mathematical Reviews number (MathSciNet)
MR2350854

Zentralblatt MATH identifier
1173.15012

Subjects
Primary: 15A52 35Q15: Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]
Secondary: 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Citation

Krasovsky, I. V. Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant. Duke Math. J. 139 (2007), no. 3, 581--619. doi:10.1215/S0012-7094-07-13936-X. https://projecteuclid.org/euclid.dmj/1187916271


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