Linear eigenvalue statistics of XX′ matrices

Article Type

Research Article

Publication Title

Journal of Mathematical Physics

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.

DOI

https://10.1063/5.0156637

Publication Date

12-1-2023

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