On orthogonal and symplectic matrix ensembles
On orthogonal and symplectic matrix ensembles
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DOI：
10.1007/bf02099545
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发表时间：
1996-04-01
影响因子：
2.4
通讯作者：
Widom, H
中科院分区：
文献类型：
--
作者：
Tracy, CA;Widom, H
本文的重点是概率，E（β）（0;J），一个集J组成的一个有限的工会的间隔不包含本征值的有限N高斯正交（β = 1）和高斯辛（β = 4）合奏和他们各自的缩放限制都在散装和边缘的频谱。我们展示了如何这些概率可以表示在相应的酉（β = 2）合奏中产生的数量。我们最明确的新结果关注的最大特征值在每个这些合奏的分布。在边缘缩放限制，我们表明，这些最大的特征值分布给出了一个特定的Painleve II功能。
The focus of this paper is on the probability, E(beta)(0;J), that a set J consisting of a finite union of intervals contains no eigenvalues for the finite N Gaussian Orthogonal (beta = 1) and Gaussian Symplectic (beta = 4) Ensembles and their respective scaling limits both in the bulk and at the edge of the spectrum. We show how these probabilities can be expressed in terms of quantities arising in the corresponding unitary (beta = 2) ensembles. Our most explicit new results concern the distribution of the largest eigenvalue in each of these ensembles. In the edge scaling limit we show that these largest eigenvalue distributions are given in terms of a particular Painleve II function.