Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices
Abstract
Consider the n × n reverse circulant RCn(t) and symmetric circulant SCn(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 ∞, 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.
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