On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble

Details On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble

2002-05-21

arxiv.org/abs/hep-th/0205215v1

Nucl.Phys. B647 (2002) 581-597

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, no figures

Scientific paper

10.1016/S0550-3213(02)00904-5

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