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Title: Fluctuations of linear eigenvalue statistics of time dependent random circulant matrices Authors:  Shambhu Nath Maurya - Indian Institute of Technology Bombay (India) [presenting]
Abstract: Fluctuations of linear eigenvalue statistics of random circulant matrices are discussed when the entries are independent Brownian motion. With polynomial test functions, we discuss the joint fluctuation and tightness of the time-dependent linear eigenvalue statistics of these matrices as the dimension of matrices goes to infinite. We see that the limit law is a Gaussian process with a nice variance structure. The methods of proofs are mainly combinatorial, based on some results of process convergence, trace formula of circulant matrix, method of moments and Wick's formula. This method can be applied to study fluctuations of linear eigenvalue statistics of other patterned random matrices, namely; Toeplitz, Hankel, reverse circulant and symmetric circulant matrices.