Process convergence of Fluctuations of linear eigenvalue statistics of\n random circulant matrices

2019/09/02 by Shambhu Nath Maurya, Maurya, Shambhu Nath, Koushik Saha +1
Computer Science · Mathematics · #60F05 #60G15 #60G57 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1909.00686

openalex publication_date 2019/09/02 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss the process convergence of the time dependent\nfluctuations of linear eigenvalue statistics of random circulant matrices with\nindependent Brownian motion entries, as the dimension of the matrix tends to\n\∞ . Our derivation is based on the trace formula of circulant matrix,\nmethod of moments and some combinatorial techniques.\n

Citations

• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices

Related

• Universality in the fluctuation of eigenvalues of random circulant matrices
• Eigenvectors of Sample Covariance Matrices: Universality of global fluctuations
• Asymptotic Behaviour of Linear eigenvalue statistics of Hankel matrices
• Partial linear eigenvalue statistics for non-Hermitian random matrices
• Fluctuations Of Linear Spectral Statistics Of Deformed Wigner Matrices