Work

Linear eigenvalue statistics of XX′ matrices

Year: 2023

Type: article

Abstract: This article focuses on the fluctuations of linear eigenvalue statistics of Tn×pTn×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 Hn×pHn×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.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0156637

Authors: Kiran Kumar A. S., Shambhu Nath Maurya, Koushik Saha

Institutions: Indian Institute of Technology Bombay, Indian Statistical Institute

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, National Board for Higher Mathematics, Indian Institute of Science Education and Research Bhopal, Indian Institute of Science Education and Research Mohali

Awards: G6321373941, G8159085165