Eigenvalue statistics of the real Ginibre ensemble.

@article{Forrester2007EigenvalueSO,
  title={Eigenvalue statistics of the real Ginibre ensemble.},
  author={Peter J. Forrester and Taro Nagao},
  journal={Physical review letters},
  year={2007},
  volume={99 5},
  pages={
          050603
        }
}
The real Ginibre ensemble consists of random N x N matrices formed from independent and identically distributed standard Gaussian entries. By using the method of skew orthogonal polynomials, the general n-point correlations for the real eigenvalues, and for the complex eigenvalues, are given as n x n Pfaffians with explicit entries. A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented. This is relevant to May's stability analysis… 

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