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On the Correlation Function of the Characteristic Polynomials of the Hermitian Wigner Ensemble

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Abstract

We consider the asymptotic of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices H n  = n −1/2 W n . We show that for the correlation function of any even order the asymptotic coincides with this for the Gaussian Unitary Ensemble up to a factor, depending only on the fourth moment of the common probability law of entries \({\mathfrak{J} W_{jk}, \mathfrak{R} W_{jk}}\) , i.e. that the higher moments do not contribute to the above limit.

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  1. Institute for Low Temperature Physics Ukr.Ac.Sci, 47 Lenin Ave., 61103, Kharkov, Ukraine

    Tatyana Shcherbina

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  1. Tatyana Shcherbina
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Correspondence to Tatyana Shcherbina.

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Communicated by P. Forrester

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Shcherbina, T. On the Correlation Function of the Characteristic Polynomials of the Hermitian Wigner Ensemble. Commun. Math. Phys. 308, 1–21 (2011). https://doi.org/10.1007/s00220-011-1316-8

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  • DOI: https://doi.org/10.1007/s00220-011-1316-8

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