Eigenvalue statistics of the real Ginibre ensemble

Details Eigenvalue statistics of the real Ginibre ensemble Eigenvalue statistics of the real Ginibre ensemble

2007-06-14

arxiv.org/abs/0706.2020v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, to appear PRL

Scientific paper

10.1103/PhysRevLett.99.050603

The real Ginibre ensemble consists of random $N \times N$ matrices formed from i.i.d. 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 $n \times n$ 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.

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