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arXiv · 0803.0926

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

F. Götze·H. Kösters
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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.

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F. Götze, H. Kösters. 2008-03-06. On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix. https://doi.org/10.1007/s00220-008-0544-z

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