Eigenstate thermalisation at the edge for Wigner matrices
Abstract
We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is optimal for any observable. This complements earlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math., Sigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv: 2303.11142) that were restricted either to the bulk of the spectrum or to special observables. As a main ingredient, we prove a new multi-resolvent local law that optimally accounts for the edge scaling.
Cite
@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}
}
Comments
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