Eigenvalue statistics of the real Ginibre ensemble.
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 of biological webs.
Forrester
Peter J
PJ
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
Nagao
Taro
T