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.
On the Second-Order Correlation Function of the Characteristic Polynomial of a Real Symmetric Wigner Matrix
Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum
Characteristic Polynomials of Sample Covariance Matrices: The Non-Square Case
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