A CLT for a band matrix model

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 combi...

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Bibliographic Details
Published inProbability theory and related fields Vol. 134; no. 2; pp. 283 - 338
Main Authors ANDERSON, Greg W, ZEITOUNI, Ofer
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.02.2006
Berlin Springer Nature B.V
New York, NY
Subjects
Combinatorial analysis
Digital Object Identifier
Eigenvalues
Enumeration
Exact sciences and technology
Limit theorems
Mathematical analysis
Mathematical functions
Mathematics
Matrices (mathematics)
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Stochastic processes
Studies
Theorems
Band matrix
Statistical method
Enumeration
Random matrix
Central limit theorem
Generating function
Symmetric matrix
Probability theory
Law of large numbers
Wishart matrix
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Summary: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. O.Z. was partially supported by NSF grant number DMS-0302230. [PUBLICATION ABSTRACT]
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-004-0422-3