Isotropic self-consistent equations for mean-field random matrices

• 成果类型: Article
• 署名作者: He, Yukun; Knowles, Antti; Rosenthal, Ron
• 署名单位: University of Geneva; Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0776-y
• 发表日期: 2018
• 页码: 203-249
• 关键词: generalized wigner matrices; local semicircle law; random band matrices; spectral statistics; Covariance matrices; bulk universality; delocalization; ENTRIES

摘要

We present a simple and versatile method for deriving (an)isotropic local laws for general random matrices constructed from independent random variables. Our method is applicable to mean-field random matrices, where all independent variables have comparable variances. It is entirely insensitive to the expectation of the matrix. In this paper we focus on the probabilistic part of the proof-the derivation of the self-consistent equations. As a concrete application, we settle in complete generality the local law for Wigner matrices with arbitrary expectation.