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Spectrum of random centrosymmetric matrices; CLT and circular law

Indrajit Jana

https://orcid.org/0000-0003-2178-4513

Department of Mathematics, Indian Institute of Technology, Bhubaneswar, Argul, Khordha 752050, Odisha, India

E-mail Address: ijana@iitbbs.ac.in

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and

Sunita Rani

https://orcid.org/0009-0001-9419-5974

Department of Mathematics, Indian Institute of Technology, Bhubaneswar, Argul, Khordha 752050, Odisha, India

E-mail Address: s21ma09007@iitbbs.ac.in

E-mail Address: sunitakurra123@gmail.com

Corresponding author.

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https://doi.org/10.1142/S2010326324500266Cited by:0 (Source: Crossref)

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.

Keywords:

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