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 a ItzyksonZuber type integral for matrices from the noncompact 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.
 Publication:

Nuclear Physics B
 Pub Date:
 December 2002
 DOI:
 10.1016/S05503213(02)009045
 arXiv:
 arXiv:hepth/0205215
 Bibcode:
 2002NuPhB.647..581F
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics
 EPrint:
 15 pages, no figures