Abstract
The integrable structure of Ginibre’s orthogonal ensemble of random matrices is looked at through the prism of the probability to find exactly real eigenvalues in the spectrum of an real asymmetric Gaussian random matrix. The exact solution for the probability function 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.
- Received 21 July 2005
DOI:https://doi.org/10.1103/PhysRevLett.95.230201
©2005 American Physical Society