Bulk universality for sparse complex non-Hermitian random matrices

• 成果类型: Article; Early Access
• 署名作者: 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; 1432-2064
• DOI: 10.1007/s00440-026-01511-y
• 发表日期: 2026-07-08
• 关键词: circular law; statistics

摘要

We prove that the local eigenvalue statistics in the bulk for complex random matrices with independent entries whose r-th absolute moment decays as N-1-(r-2)& varepsilon; for some & varepsilon;>0 are universal. This includes sparse matrices whose entries are the product of a Bernouilli random variable with mean N-1+& varepsilon; and an independent complex-valued random variable. By a standard truncation argument, we can also conclude universality for complex random matrices with 4+& varepsilon; moments. The main ingredient is a sparse multi-resolvent local law for products involving any finite number of resolvents of the Hermitisation and deterministic 2N & times;2N matrices whose N & times;N blocks are multiples of the identity.