Fluctuations of linear eigenvalue statistics of reverse circulant and symmetric circulant matrices with independent entries

In this article, we study the fluctuations of linear eigenvalue statistics of reverse circulant (RCn) and symmetric circulant (SCn) matrices with independent entries that satisfy some moment conditions. We show that 1nTrϕ(RCn) and 1nTrϕ(SCn) obey the central limit theorem type result, where ϕ is a polynomial test function.