A CLT for a band matrix model

2004/12/02 by Greg W. Anderson, Greg Anderson, Anderson, Greg +2 · 2 citations
Mathematics · #15A52 #60F05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:15A52 #msc:60F05

paper · pdf · doi:10.48550/arxiv.math/0412040

To appear, Prob. Theory Rel. Fields

arxiv created 2004/12/02 · openalex publication_date 2004/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poincare type. Special cases treated, with an explicit evaluation of limiting variances, are generalized Wigner and Wishart matrices.

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• Tridiagonal random matrices, an analytic approach
• CLT for LES of real valued random centrosymmetric matrices

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