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

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<[beta]<4) and at the edge ([beta]>0). Analogs have recently been studied by Götze and Kösters for general Hermitian (real) Wigner matrices.