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arXiv · 0706.2020

Eigenvalue statistics of the real Ginibre ensemble

Peter J. Forrester·Taro Nagao
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Abstract

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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BibTeXRIS

Peter J. Forrester, Taro Nagao. 2007-06-14. Eigenvalue statistics of the real Ginibre ensemble. https://doi.org/10.1103/physrevlett.99.050603

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