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

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

2004-11-04

arxiv.org/abs/math-ph/0411016v4

Physics

Mathematical Physics

35 pages, 5 figures

Scientific paper

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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