A CLT for a band matrix model

• 成果类型: Article
• 署名作者: Anderson, GW; Zeitouni, O
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Technion Israel Institute of Technology; Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0422-3
• 发表日期: 2006
• 页码: 283-338
• 关键词: limit-theorems; eigenvalues; fluctuations; statistics

摘要

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.