NORMAL FLUCTUATION IN QUANTUM ERGODICITY FOR WIGNER MATRICES

• 成果类型: Article
• 署名作者: Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
• 署名单位: Princeton University; Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1552
• 发表日期: 2022
• 页码: 984-1012
• 关键词: fixed-energy universality; generalized wigner; statistical-mechanics; unique ergodicity; eigenvectors; chaos

摘要

We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N x N Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws.