Bulk universality for complex non-Hermitian matrices with independent and identically distributed entries

• 成果类型: Article
• 署名作者: Maltsev, Anna; Osman, Mohammed
• 署名单位: University of London; Queen Mary University London
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01321-0
• 发表日期: 2025
• 页码: 289-334
• 关键词: ensembles; statistics; real

摘要

We consider NxN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\times N$$\end{document} matrices with complex entries that are perturbed by a complex Gaussian matrix with small variance. We prove that if the unperturbed matrix satisfies certain local laws then the bulk correlation functions are universal in the large N limit. Assuming the entries are independent and identically distributed (iid) with a common distribution that has finite moments, the Gaussian component is removed by the four moment theorem of Tao and Vu.