A CLT for a band matrix model

Details A CLT for a band matrix model A CLT for a band matrix model

2004-12-02

arxiv.org/abs/math/0412040v1

Mathematics

Probability

To appear, Prob. Theory Rel. Fields

Scientific paper

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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