No eigenvalues outside the support of the limiting spectral distribution of quaternion sample covariance matrices

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2020-10-01 DOI:10.1142/s2010326321500039

Huiqin Li

引用次数: 6

Abstract

In this paper, we consider the spectral properties of quaternion sample covariance matrices. Let [Formula: see text], where [Formula: see text] is the square root of a [Formula: see text] quaternion Hermitian non-negative definite matrix [Formula: see text] and [Formula: see text] is a [Formula: see text] matrix consisting of i.i.d. standard quaternion entries. Under the framework of random matrix theory, i.e. [Formula: see text] as [Formula: see text], we prove that if the fourth moment of the entries is finite, then there will almost surely be no eigenvalues that appear in any closed interval outside the support of the limiting distribution as [Formula: see text].

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在四元数样本协方差矩阵的极限谱分布支持之外没有特征值

本文研究了四元数样本协方差矩阵的谱性质。设[公式:见文]，其中[公式:见文]是[公式:见文]四元数的平方根[公式:见文]厄米非负定矩阵[公式:见文]，[公式:见文]是由i.d个标准四元数项组成的[公式:见文]矩阵。在随机矩阵理论的框架下，即[公式:见文]为[公式:见文]，我们证明了如果条目的第四阶矩是有限的，那么在极限分布支持之外的任何封闭区间内几乎肯定不会出现特征值[公式:见文]。

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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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.