Correlation functions, cluster functions, and spacing distributions for random matrices
Correlation functions, cluster functions, and spacing distributions for random matrices
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DOI：
10.1023/a:1023084324803
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发表时间：
1998-09-01
影响因子：
1.6
通讯作者：
Widom, H
中科院分区：
文献类型：
--
作者：
Tracy, CA;Widom, H
正交和辛矩阵模型中相关函数的常用公式将它们表示为四元数行列式。从这一表示中，我们可以根据矩阵值核的 Fredholm 行列式推导出间距概率的公式。各个公式的推导都有些涉及。在本文中，我们提出了一种直接方法，该方法立即导致酉系综的标量核和正交系综和辛系综的矩阵核，以及相关函数、簇函数和间距分布的表示。
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles, and the representations of the correlation functions, cluster functions, and spacing distributions in terms of them.