Process convergence of Fluctuations of linear eigenvalue statistics of random circulant matrices

Abstract

In this paper we discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to $\infty$. Our derivation is based on the trace formula of circulant matrix, method of moments and some combinatorial techniques.

27 pages, 4 figures