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Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices
Journal
Journal of Mathematical Physics
ISSN
00222488
Date Issued
2022-03-01
Author(s)
Bose, Arup
Maurya, Shambhu Nath
Saha, Koushik
Abstract
We consider the n × n reverse circulant and symmetric circulant random matrices with independent Brownian motion entries. With polynomial test functions φ, we discuss the joint fluctuation and tightness (in t and φ) of the time dependent linear eigenvalue statistics of these matrices as n → ∞ and show convergence to appropriate Gaussian processes. The proofs are mainly combinatorial.