THE CIRCULAR LAW FOR RANDOM MATRICES

• 成果类型: Article
• 署名作者: Gotze, Friedrich; Tikhomirov, Alexander
• 署名单位: University of Bielefeld; Saint Petersburg State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09.AOP522
• 发表日期: 2010
• 页码: 1444-1491
• 关键词: invertibility

摘要

We consider the joint distribution of real and imaginary parts of eigen-values of random matrices with Independent entries with mean zero and unit variance We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries We assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices The results are based on previous work of Bai, Rudelson and the authors extending those results to a larger class of sparse matrices