A First Szegő's Limit Theorem for a class of non-Toeplitz matrices

2015/11/18 by Alain Bourget, Bourget, A., Tyler McMillen +1
Computer Science · Engineering · Mathematics · #15B05 #35P20 #41A60 #47B35 #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Point processes and geometric inequalities #Random Matrices and Applications #Spectral Theory (math.SP) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1511.06020

openalex publication_date 2015/11/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are μ-distributed for some probability measure. As an application of our results, we extend the well-known class of Kac-Murdock-Szegő generalized Toeplitz matrices to sequences of matrices whose diagonal entries are modeled by Riemann integrable functions.

Citations

• Locally Toeplitz sequences: spectral properties and applications
• Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations

Related

• Spectral asymptotics for Kac-Murdock-Szegő matrices
• On the asymptotic eigenvalue distribution of Toeplitz matrices
• Szego limit theorems
• Free versions of the strong Szegő limit theorem
• An equilibrium problem for the limiting eigenvalue distribution of banded Toeplitz matrices