Eigenvalue statistics of the real Ginibre ensemble
Statistical Mechanics
2015-06-16 v1
Abstract
The real Ginibre ensemble consists of random matrices formed from i.i.d. standard Gaussian entries. By using the method of skew orthogonal polynomials, the general -point correlations for the real eigenvalues, and for the complex eigenvalues, are given as 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.
Keywords
Cite
@article{arxiv.0706.2020,
title = {Eigenvalue statistics of the real Ginibre ensemble},
author = {Peter J. Forrester and Taro Nagao},
journal= {arXiv preprint arXiv:0706.2020},
year = {2015}
}