A CLT for a band matrix model

被引：131

作者：

Anderson, GW

Zeitouni, O

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[3] Technion Israel Inst Technol, Dept EE, IL-32000 Haifa, Israel

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2006年 / 134卷 / 02期

关键词：

D O I：

10.1007/s00440-004-0422-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：283 / 338

页数：56

共 29 条

[1]

Bai ZD, 1999, STAT SINICA, V9, P611

[2]

Bai ZD, 2004, ANN PROBAB, V32, P553

[3]

BAI ZD, 2003, CONVERGENCE SPECTRAL

[4]

Bobkov S. G., 1999, VESTN SYKTYVKAR U SE, V3, P15

[5]

BOROVKOV AA, 1983, THEOR PROBAB APPL, V28, P209

[6] Fluctuations of empirical laws of large random matrices [J].

Cabanal-Duvillard, T .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2001, 37 (03) :373-402

[7]

CHATTERJEE S, 2004, NEW METHOD BOUNDING

[8]

Deift P., 2000, ORTHOGONAL POLYNOMIA

[9] THE EIGENVALUES OF RANDOM SYMMETRIC-MATRICES [J].

FUREDI, Z ;

KOMLOS, J .

COMBINATORICA, 1981, 1 (03) :233-241

[10]

Girko V. L., 1990, THEORY RANDOM DETERM

← 1 2 3 →