Wigner 矩阵在谱边缘的本征态热化
概率论
2024-12-18 v4 数学物理
math.MP
摘要
我们证明了 Wigner 矩阵的本征态热化假说在整个谱上一致成立，特别是在谱边缘附近，且对任一可观测量具有最优的涨落界。这补充了 Cipolloni 等人（Comm. Math. Phys. 388, 2021; Forum Math., Sigma 10, 2022）与 Benigni 等人（Comm. Math. Phys. 391, 2022; arXiv: 2303.11142）的早期工作，那些工作要么限于谱的体态，要么限于特殊可观测量。作为主要要素，我们证明了一个新的多 resolvent 局域定律，最优地考虑了边缘标度。
引用
@article{arxiv.2309.05488,
title = {Eigenstate thermalisation at the edge for Wigner matrices},
author = {Giorgio Cipolloni and László Erdős and Joscha Henheik},
journal= {arXiv preprint arXiv:2309.05488},
year = {2024}
}
备注
46 pages, 1 figure. v1 --> v2: Added a missing factor in Proposition 3.1; v2 --> v3: Fixed typos and streamlined the setup of Proposition 4.3 by directly incorporating the reduction inequalities (Lemma 4.6) into the master inequalities; v3 --> v4: Minor corrections and added further explanations