Eigenvalue statistics of the real Ginibre ensemble |
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Authors: | Forrester Peter J Nagao Taro |
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Institution: | Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia. |
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Abstract: | 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. |
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