Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-16
J.Phys.A36:3411-3424,2003
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, 1 figure, LaTeX, submitted to J. Phys. A special issue on random matrices, minor corrections, references added
Scientific paper
10.1088/0305-4470/36/12/332
We compute the large scale (macroscopic) correlations in ensembles of normal random matrices with an arbitrary measure and in ensembles of general non-Hermition matrices with a class of non-Gaussian measures. In both cases the eigenvalues are complex and in the large $N$ limit they occupy a domain in the complex plane. For the case when the support of eigenvalues is a connected compact domain, we compute two-, three- and four-point connected correlation functions in the first non-vanishing order in 1/N in a manner that the algorithm of computing higher correlations becomes clear. The correlation functions are expressed through the solution of the Dirichlet boundary problem in the domain complementary to the support of eigenvalues. The two-point correlation functions are shown to be universal in the sense that they depend only on the support of eigenvalues and are expressed through the Dirichlet Green function of its complement.
Wiegmann Paul
Zabrodin Anton
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