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

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

2008-03-06

arxiv.org/abs/0803.0926v1

Mathematics

Probability

20 pages

Scientific paper

10.1007/s00220-008-0544-z

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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