  This article deals with the limiting spectral distribution and joint
convergence of reverse circulant and symmetric circulant matrices with
independent entries. These results are already proved in articles Bose and Sen
(2008) \cite{bose_sen_LSD_EJP}, and Bose, Hazra and Saha (2011)
\cite{bose_saha_patter_JC_annals}, respectively. But this article provides
alternate proofs of these results which are shorter than the existing proofs.
Our method is mainly based on moment method.
