Large scale correlations in normal and general non-Hermitian matrix ensembles

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dc.creatorWiegmann, P.
dc.creatorZabrodin, A.
dc.date2002-10-16
dc.date2003-01-29
dc.date.accessioned2026-07-07T10:49:29Z
dc.date.available2026-07-07T10:49:29Z
dc.descriptionWe 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.
dc.description16 pages, 1 figure, LaTeX, submitted to J. Phys. A special issue on random matrices, minor corrections, references added
dc.identifierhttps://arxiv.org/abs/hep-th/0210159
dc.identifierhttp://arxiv.org/abs/hep-th/0210159
dc.identifierJ.Phys.A36:3411-3424,2003
dc.identifierdoi:10.1088/0305-4470/36/12/332
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184234
dc.subjectHigh Energy Physics - Theory
dc.subjectMesoscale and Nanoscale Physics
dc.titleLarge scale correlations in normal and general non-Hermitian matrix ensembles
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