A CLT for a band matrix model
Probability
2007-05-23 v1 Combinatorics
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.
Cite
@article{arxiv.math/0412040,
title = {A CLT for a band matrix model},
author = {Greg Anderson and Ofer Zeitouni},
journal= {arXiv preprint arXiv:math/0412040},
year = {2007}
}
Comments
To appear, Prob. Theory Rel. Fields