Single eigenvalue fluctuations of general Wigner-type matrices

• 成果类型: Article
• 署名作者: Landon, Benjamin; Lopatto, Patrick; Sosoe, Philippe
• 署名单位: University of Toronto; Brown University; Cornell University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01181-6
• 发表日期: 2024
• 页码: 1-62
• 关键词: CENTRAL-LIMIT-THEOREM; fixed-energy universality; statistical-theory; linear statistics; RIGIDITY; density

摘要

We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue around its classical location are Gaussian with a universal variance. Our method is based on a dynamical approach to mesoscopic linear spectral statistics which reduces their behavior on short scales to that on larger scales. We prove a central limit theorem for linear spectral statistics on larger scales via resolvent techniques and show that for certain classes of test functions, the leading-order contribution to the variance agrees with the GOE/GUE cases.