On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble
Abstract
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 an 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 generalising the known expressions for only positive moments. Finally, we present the asymptotic formula for the correlation function in the large matrix size limit.
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