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 $(S{C}_n)$ with independent entries which satisfy some moment conditions. We show that $\frac{1}{\sqrt{n}} \Tr ϕ(SC_n)$ obey the central limit theorem (CLT) type result, where $\varphi$ is a nice test function.

arXiv comment19 pages

References in corpus (4)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Fluctuations of Linear Eigenvalue Statistics of Random Band Matrices
• Fluctuations of eigenvalues of patterned random matrices

Cited by in corpus (1)

• Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices