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Linear eigenvalue statistics of XX′ matrices.

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Název: Linear eigenvalue statistics of XX′ matrices.
Autoři: A. S., Kiran Kumar, Maurya, Shambhu Nath, Saha, Koushik
Zdroj: Journal of Mathematical Physics; Dec2023, Vol. 64 Issue 12, p1-27, 27p
Témata: TOEPLITZ matrices, STATISTICS, MATRICES (Mathematics), RANDOM variables, GAUSSIAN distribution
Abstrakt: 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]
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Databáze: Complementary Index
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Abstrakt:This article focuses on the fluctuations of linear eigenvalue statistics of T n × p T n × p ′ , where T<subscript>n×p</subscript> 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 H<subscript>n×p</subscript> 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]
ISSN:00222488
DOI:10.1063/5.0156637