Local circular law for random matrices

• 成果类型: Article
• 署名作者: Bourgade, Paul; Yau, Horng-Tzer; Yin, Jun
• 署名单位: Harvard University; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0514-z
• 发表日期: 2014
• 页码: 545-595
• 关键词: invertibility; eigenvalues

摘要

The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point away from the unit circle. More precisely, if for arbitrarily small , the circular law is valid around up to scale for any under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition.