On the behavior of large empirical autocovariance matrices between the past and the future

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2019-11-20 DOI:10.1142/s2010326321500210

P. Loubaton, D. Tieplova

引用次数: 0

Abstract

The asymptotic behavior of the distribution of the squared singular values of the sample autocovariance matrix between the past and the future of a high-dimensional complex Gaussian uncorrelated sequence is studied. Using Gaussian tools, it is established that the distribution behaves as a deterministic probability measure whose support [Formula: see text] is characterized. It is also established that the squared singular values are almost surely located in a neighborhood of [Formula: see text].

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在过去和未来之间的大经验自协方差矩阵的行为

研究了一类高维复高斯不相关序列的样本自协方差矩阵的过去和未来之间的奇异值平方分布的渐近性质。利用高斯工具，建立了该分布表现为一个确定性概率测度，其支持度[公式:见文]被表征。还确定了平方奇异值几乎肯定位于[公式:见文]的邻域中。

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.