A CLT for a band matrix model

Preprint

2 December 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0412040

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.

Keywords

CONCENTRATION INEQUALITIES
EXPLICIT EVALUATION
WISHART MATRICES
POINCARE TYPE
LIMIT THEOREM
MATRIX MODEL
BAND MATRIX
VARIANCES
CLT

All Related Versions

Version 1, 2004-12-02, ArXiv

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