Fluctuations of eigenvalues of patterned random matrices

Abstract

In this article we study the fluctuation of linear statistics of eigenvalues of circulant, symmetric circulant, reverse circulant and Hankel matrices. We show that the linear spectral statistics of these matrices converges to the Gaussian distribution in total variation norm when the matrices are constructed using i.i.d. normal random variables. We also calculate the limiting variance of the linear spectral statistics for circulant, symmetric circulant and reverse circulant matrices.

25 pages, Statements and proofs of Theorems 4, 5 and 6 have been modified

References in corpus (5)

• 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
• On fluctuations of eigenvalues of random band matrices
• Convergence of joint moments for independent random patterned matrices

Cited by in corpus (6)

• Fluctuation of linear eigenvalue statistics of reverse circulant matrices with independent entries
• Spectrum of random centrosymmetric matrices; CLT and Circular law
• Fluctuation of eigenvalues of symmetric circulant matrices with independent entries
• Patterned Random Matrices: deviations from universality
• Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices
• Process convergence of Fluctuations of linear eigenvalue statistics of random circulant matrices