Fluctuation of eigenvalues of symmetric circulant matrices with independent entries

Abstract

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