On the second-order correlation of characteristic polynomials of Hermite ββ ensembles

Consider the Hermite ββ 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<β<40<β<4) and at the edge (β>0β>0). Analogs have recently been studied by Götze and Kösters for general Hermitian (real) Wigner matrices.