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 $N\times N$ 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 $\mathsf{Gl}(\mathsf{n},\mathcal{C})/U(1)\times ...\times \mathsf{U}(1)$ (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.

15 pages, no figures

References in corpus (2)

• Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
• Microscopic correlation functions for the QCD Dirac operator with chemical potential

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