On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble

We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N× N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding a Itzykson-Zuber type integral for matrices from the non-compact manifold Gl(n, C)/ U(1)×⋯× U(1) (matrix Macdonald function). The correlation function is shown to be always represented in a determinant form generalizing the known expressions for only positive moments. Finally, we present the asymptotic formula for the correlation function in the large matrix size limit.