一类由Hadamard积构成的大维随机矩阵的极限特征值行为

Pub Date : 2021-12-08 DOI:10.1142/s2010326322500502

J. W. Silverstein

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引用次数: 1

摘要

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，

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

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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