On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble

Yan V Fyodorov; Eugene Strahov

doi:10.1016/s0550-3213(02)00904-5

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On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble

Yan V Fyodorov·Eugene Strahov

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

Yan V Fyodorov, Eugene Strahov. 2002-05-21. On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble. https://doi.org/10.1016/s0550-3213(02)00904-5

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