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

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