Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
Kanzieper, Eugene ; Akemann, Gernot
arXiv, 0507058 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-07-21
Classification:  Mathematical Physics,  Condensed Matter - Disordered Systems and Neural Networks,  High Energy Physics - Theory,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0507058,
     author = {Kanzieper, Eugene and Akemann, Gernot},
     title = {Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real
  Matrices},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0507058}
}

Kanzieper, Eugene; Akemann, Gernot. Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real
  Matrices. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0507058/