Limiting Eigenvalue Behavior of a Class of Large Dimensional Random Matrices Formed From a Hadamard Product

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2021-12-08 DOI:10.1142/s2010326322500502

J. W. Silverstein

引用次数: 1

Abstract

This paper investigates the strong limiting behavior of the eigenvalues of the class of matrices 1 N (Dn ◦Xn)(Dn ◦Xn)∗, studied in Girko 2001. Here, Xn = (xij) is an n×N random matrix consisting of independent complex standardized random variables, Dn = (dij), n × N , has nonnegative entries, and ◦ denotes Hadamard (componentwise) product. Results are obtained under assumptions on the entries of Xn and Dn which are different from those in Girko (2001), which include a Lindeberg condition on the entries of Dn ◦Xn, as well as a bound on the average of the rows and columns of Dn ◦ Dn. The present paper separates the assumptions needed on Xn and Dn. It assumes a Lindeberg condition on the entries of Xn, along with a tigntness-like condition on the entries of Dn,

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一类由Hadamard积构成的大维随机矩阵的极限特征值行为

本文研究了一类矩阵1 N (Dn◦Xn)(Dn◦Xn) * (Girko 2001) *的特征值的强极限性。其中，Xn = (xij)是由独立的复标准化随机变量组成的n×N随机矩阵，Dn = (dij)， n× n具有非负项，◦表示Hadamard (component - wise)积。结果与Girko(2001)对Xn和Dn表项的假设不同，包括对Dn◦Xn表项的Lindeberg条件，以及对Dn◦Dn的行和列平均值的定界。本文分离了Xn和Dn所需的假设。它假设Xn的元素有林德伯格条件，同时对Dn的元素也有类似紧度的条件，

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.