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On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix

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Abstract

We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for a general Hermitian Wigner matrix. Our proofs rely on an explicit formula for the exponential generating function of the second-order correlation function of the characteristic polynomial. Furthermore, we show that the second-order correlation function of the characteristic polynomial is closely related to that of the permanental polynomial.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    F. Götze & H. Kösters

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  1. F. Götze
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  2. H. Kösters
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Correspondence to H. Kösters.

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Communicated by H. Spohn

Supported by CRC 701 “Spectral Structures and Topological Methods in Mathematics”.

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Götze, F., Kösters, H. On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. Commun. Math. Phys. 285, 1183–1205 (2009). https://doi.org/10.1007/s00220-008-0544-z

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  • DOI: https://doi.org/10.1007/s00220-008-0544-z

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