Forrester Peter J, Nagao Taro
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
Phys Rev Lett. 2007 Aug 3;99(5):050603. doi: 10.1103/PhysRevLett.99.050603.
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.
实 Ginibre 系综由由独立同分布的标准高斯元素构成的随机 N×N 矩阵组成。通过使用斜正交多项式方法，给出了实特征值和复特征值的一般 n 点关联，其形式为具有明确元素的 n×n Pfaff 式。给出了最大实特征值的累积概率密度的一个易于计算的公式。这与梅对生物网络的稳定性分析相关。
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