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Anderson, Greg W.; Zeitouni, Ofer

A CLT for a band matrix model. (English) Zbl 1084.60014

Probab. Theory Relat. Fields 134, No. 2, 283-338 (2006).
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 Poincaré type. Special cases treated, with an explicit evaluation of limiting variances, are generalized Wigner and Wishart matrices.

Cited in 91 Documents

MSC:

60F05 Central limit and other weak theorems
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\textit{G. W. Anderson} and \textit{O. Zeitouni}, Probab. Theory Relat. Fields 134, No. 2, 283--338 (2006; Zbl 1084.60014)
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References:

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