Work

Spectrum of random centrosymmetric matrices; CLT and circular law

Year: 2024

Type: article

Abstract: In this paper, we analyze the asymptotic fluctuations of linear eigenvalue statistics of random centrosymmetric matrices with i.i.d. entries. We prove that for a complex analytic test function, the centered and normalized linear eigenvalue statistics of random centrosymmetric matrices converge to a normal distribution. We find the exact expression of the variance of the limiting normal distribution via combinatorial arguments. Moreover, we argue that the limiting spectral distribution of properly scaled centrosymmetric matrices follows the circular law.

Source: Random Matrices Theory and Application

DOI: 10.1142/s2010326324500266

Authors: Indrajit Jana, Sunita Rani

Institution: Indian Institute of Technology Bhubaneswar

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, University Grants Commission

Awards: G3692813985, G6417678755