Rate of convergence to the semi-circular law

• 成果类型: Article
• 署名作者: Götze, F; Tikhomirov, A
• 署名单位: University of Bielefeld; Syktyvkar State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0285-z
• 发表日期: 2003
• 页码: 228-276
• 关键词: spectral distributions; RANDOM MATRICES

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.