Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices

Abstract

Consider the $n\times n$ reverse circulant $R{C}_n(t)$ and symmetric circulant $S{C}_n(t)$ matrices with independent Brownian motion entries. We discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of these matrices as $n \tends \infty$, when the test functions of the statistics are polynomials. The proofs are mainly combinatorial, based on the trace formula, method of moments and some results on process convergence.

36 pages, 0 figure

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
• Fluctuation of linear eigenvalue statistics of reverse circulant matrices with independent entries
• Fluctuation of eigenvalues of symmetric circulant matrices with independent entries