Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices

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dc.creatorKanzieper, Eugene
dc.creatorAkemann, Gernot
dc.date2005-07-21
dc.date2005-11-29
dc.date.accessioned2026-07-07T06:42:17Z
dc.date.available2026-07-07T06:42:17Z
dc.descriptionThe integrable structure of Ginibre's Orthogonal Ensemble of random matrices is looked at through the prism of the probability "p_{n,k}" to find exactly "k" real eigenvalues in the spectrum of an "n" by "n" real asymmetric Gaussian random matrix. The exact solution for the probability function "p_{n,k}" is presented, and its remarkable connection to the theory of symmetric functions is revealed. An extension of the Dyson integration theorem is a key ingredient of the theory presented.
dc.descriptionPublished version (4.5 pages, 1 table; title changed, corrected typos)
dc.identifierhttps://arxiv.org/abs/math-ph/0507058
dc.identifierhttp://arxiv.org/abs/math-ph/0507058
dc.identifierPhys.Rev.Lett. 95 (2005) 230201
dc.identifierdoi:10.1103/PhysRevLett.95.230201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101986
dc.subjectMathematical Physics
dc.subjectDisordered Systems and Neural Networks
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.titleStatistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
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