Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
Mathematical Physics
2007-05-23 v2 Disordered Systems and Neural Networks
High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0507058,
title = {Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices},
author = {Eugene Kanzieper and Gernot Akemann},
journal= {arXiv preprint arXiv:math-ph/0507058},
year = {2007}
}
Comments
Published version (4.5 pages, 1 table; title changed, corrected typos)