  In this article we study the fluctuation of linear statistics of eigenvalues
of circulant, symmetric circulant, reverse circulant and Hankel matrices. We
show that the linear spectral statistics of these matrices converges to the
Gaussian distribution in total variation norm when the matrices are constructed
using i.i.d. normal random variables. We also calculate the limiting variance
of the linear spectral statistics for circulant, symmetric circulant and
reverse circulant matrices.
