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

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

2005-07-21

arxiv.org/abs/math-ph/0507058v2

Phys.Rev.Lett. 95 (2005) 230201

Physics

Mathematical Physics

Published version (4.5 pages, 1 table; title changed, corrected typos)

Scientific paper

10.1103/PhysRevLett.95.230201

The 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.

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