TY - JOUR
T1 - A CLT for a band matrix model
AU - Anderson, Greg W.
AU - Zeitouni, Ofer
PY - 2006/2
Y1 - 2006/2
N2 - 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.
AB - 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.
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U2 - 10.1007/s00440-004-0422-3
DO - 10.1007/s00440-004-0422-3
M3 - Article
AN - SCOPUS:28644444644
SN - 0178-8051
VL - 134
SP - 283
EP - 338
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 2
ER -