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Linear eigenvalue statistics of XX′ matrices.

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Bibliographic Details
Title:	Linear eigenvalue statistics of XX′ matrices.
Authors:	A. S., Kiran Kumar, Maurya, Shambhu Nath, Saha, Koushik
Source:	Journal of Mathematical Physics; Dec2023, Vol. 64 Issue 12, p1-27, 27p
Subject Terms:	TOEPLITZ matrices, STATISTICS, MATRICES (Mathematics), RANDOM variables, GAUSSIAN distribution
Abstract:	This article focuses on the fluctuations of linear eigenvalue statistics of T n × p T n × p ′ , where Tn×p is an n × p Toeplitz matrix with real, complex, or time-dependent entries. We show that as n → ∞ with p/n → λ ∈ (0, ∞), the linear eigenvalue statistics of these matrices for polynomial test functions converge in distribution to Gaussian random variables. We also discuss the linear eigenvalue statistics of H n × p H n × p ′ , when Hn×p is an n × p Hankel matrix. As a result of our studies, we derive in-probability limit and a central limit theorem type result for the Schettan norm of rectangular Toeplitz matrices. To establish the results, we use the method of moments. [ABSTRACT FROM AUTHOR]
	Copyright of Journal of Mathematical Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Complementary Index

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