Spectrum of random centrosymmetric matrices; CLT and Circular law
Probability
2025-10-20 v3 Mathematical Physics
math.MP
Abstract
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 also argue that the limiting spectral distribution of properly scaled centrosymmetric matrices follows the circular law.
Keywords
Cite
@article{arxiv.2403.03513,
title = {Spectrum of random centrosymmetric matrices; CLT and Circular law},
author = {Indrajit Jana and Sunita Rani},
journal= {arXiv preprint arXiv:2403.03513},
year = {2025}
}
Comments
Minor corrections. Accepted in Random Matrices: Theory and Applications