广义异质超几何函数与椭圆Wishart矩阵最大特征值的分布

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2021-04-26 DOI:10.1142/s2010326322500344

A. Shinozaki, Koki Shimizu, Hiroki Hashiguchi

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引用次数: 2

摘要

本文导出了椭圆模型下奇异Wishart矩阵特征值的精确分布。定义了具有两个矩阵参数的广义异质超几何函数，并给出了这些函数的收敛条件。用这些函数表示了奇异椭圆Wishart矩阵的特征值联合密度和最大特征值的分布函数。在矩阵-变量[公式:见文本]和Kotz型模型下进行了最大特征值分布的数值计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Generalized heterogeneous hypergeometric functions and the distribution of the largest eigenvalue of an elliptical Wishart matrix

In this paper, we derive the exact distributions of eigenvalues of a singular Wishart matrix under the elliptical model. We define the generalized heterogeneous hypergeometric functions with two matrix arguments and provide the convergence conditions of these functions. The joint density of eigenvalues and the distribution function of the largest eigenvalue for a singular elliptical Wishart matrix are represented with these functions. Numerical computations for the distribution of the largest eigenvalue are conducted under the matrix-variate [Formula: see text] and Kotz type models.

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.