Non-Hermitian spectral universality at critical points

• 成果类型: Article; Early Access
• 署名作者: Cipolloni, Giorgio; Erdos, Laszlo; Ji, Hong Chang
• 署名单位: Institute of Science & Technology - Austria; University of Arizona; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01384-7
• 发表日期: 2025
• 关键词: random matrices universality; statistics; edge

摘要

For general large non-Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A+X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A+X$$\end{document} close to the critical edge points of its spectrum are universal. This concludes the proof of the third and last remaining typical universality class for non-Hermitian random matrices (for normal deformations), after bulk and sharp edge universalities have been established in recent years.