SUBORDINATION FOR THE SUM OF TWO RANDOM MATRICES

• 成果类型: Article
• 署名作者: Kargin, V.
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP929
• 发表日期: 2015
• 页码: 2119-2150
• 关键词: finite rank deformations; LARGEST EIGENVALUE; free convolution; wigner matrices; perturbations; eigenvectors; LAW

摘要

This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in the subordination relation for the traces of the resolvents. This allows us to prove a local limit law for eigenvalues and a delocalization result for eigenvectors of the sum of two random matrices. In addition, we use subordination to determine the limit of the largest eigenvalue for the rank-one deformations of unitary-invariant random matrices.