Stability of the matrix Dyson equation and random matrices with correlations

• 成果类型: Article
• 署名作者: Ajanki, Oskari H.; Erdos, Laszlo; Krueger, Torben
• 署名单位: Institute of Science & Technology - Austria
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0835-z
• 发表日期: 2019
• 页码: 293-373
• 关键词: bulk universality; statistics; models; LAW

摘要

We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.