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

Tatyana Shcherbina

doi:10.1007/s00220-011-1316-8

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

Tatyana Shcherbina

Mathematics

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12 Scopus citations

Abstract

We consider the asymptotic of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices H_n = n^-1/2W_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 E W_jk, R W_jk, i. e. that the higher moments do not contribute to the above limit.

Original language	English (US)
Pages (from-to)	1-21
Number of pages	21
Journal	Communications In Mathematical Physics
Volume	308
Issue number	1
DOIs	https://doi.org/10.1007/s00220-011-1316-8
State	Published - Nov 2011

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-011-1316-8

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abstract = "We consider the asymptotic of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices Hn = n-1/2Wn. 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 E Wjk, R Wjk, i. e. that the higher moments do not contribute to the above limit.",

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AB - We consider the asymptotic of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices Hn = n-1/2Wn. 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 E Wjk, R Wjk, i. e. that the higher moments do not contribute to the above limit.

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

Abstract

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