A CLT for a band matrix model |
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Authors: | Greg W Anderson Ofer Zeitouni |
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Institution: | (1) School of Mathematics, University of Minnesota, 206 Church St, SE, Minneapolis, MN 55455, USA;(2) Departments of Mathematics and of EE, Technion, Haifa, 32000, Israel |
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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 Poincaré 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. |
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Keywords: | |
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