RANDOM DOUBLY STOCHASTIC MATRICES: THE CIRCULAR LAW

• 成果类型: Article
• 署名作者: Nguyen, Hoi H.
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP877
• 发表日期: 2014
• 页码: 1161-1196
• 关键词: LITTLEWOOD-OFFORD PROBLEM; permanent estimators; symmetric-matrices; UNIVERSALITY; number; distributions; eigenvalues; statistics; vectors

摘要

Let X be a matrix sampled uniformly from the set of doubly stochastic matrices of size n x n. We show that the empirical spectral distribution of the normalized matrix root n(X - EX) converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.