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On the second-order correlation of characteristic polynomials of Hermite [beta] ensembles

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Abstract

Consider the Hermite [beta] ensemble, a variant of the classical Gaussian unitary ensemble. Using Dumitriu and Edelman's matrix model representation, we first calculate the generating function of the second-order correlation of characteristic polynomials. Then we obtain the asymptotic behaviors of the second-order correlation of characteristic polynomials both in the bulk (0 0). Analogs have recently been studied by Götze and Kösters for general Hermitian (real) Wigner matrices.

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