Rate of convergence to the semi-circular law

被引：49

作者：

Götze, F

Tikhomirov, A

机构：

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld 1, Germany

[2] Syktyvkar Univ, Fac Math, Syktyvkar 167001, Russia

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2003年 / 127卷 / 02期

关键词：

independent random variables; spectral distribution; random matrix;

D O I：

10.1007/s00440-003-0285-z

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];

摘要：

A stochastic bound of order Op(n(-1/2)) for the Kolmogorov distance between the spectral distribution function of an n x n matrix from Wigner ensemble and the distribution function of the semi-circular law is obtained. The result holds assuming that the twelfth moment of the entries of the matrix is uniformly bounded.

引用

页码：228 / 276

页数：49

共 18 条

[1]

ON ASYMPTOTIC DISTRIBUTION OF EIGENVALUES OF RANDOM MATRICES [J].