Statistics of real eigenvalues in Ginibre's ensemble of random real matrices.
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 x 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.
Kanzieper
Eugene
E
Department of Applied Mathematics, Holon Academic Institute of Technology, Holon 58102, Israel.
Akemann
Gernot
G