Fluctuation of linear eigenvalue statistics of reverse circulant matrices with independent entries

Abstract

In this article, we study the fluctuations of linear eigenvalue statistics of reverse circulant $(RC_n)$ matrices with independent entries which satisfy some moment conditions. We show that $\frac{1}{\sqrt{n}} \text{Tr} \phi(RC_n)$ obey the central limit theorem (CLT) type result, where $\phi$ is a nice test function.