OPTIMAL CORRECTOR ESTIMATES ON PERCOLATION CLUSTER

• 成果类型: Article
• 署名作者: Dario, Paul
• 署名单位: Tel Aviv University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1593
• 发表日期: 2021
• 页码: 377-431
• 关键词: quenched invariance-principles; random conductance model; simple random-walk; Stochastic Homogenization; large deviations; quantitative homogenization; elliptic-equations; degenerate; discrete; bounds

摘要

We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in dimension larger than 3 and have logarithmic growth in dimension 2 in the sense of stretched exponential moments. The main ingredients are a renormalization scheme of the supercritical percolation cluster, following the works of Pisztora (Probab. Theory Related Fields 104 (1996) 427-466); large-scale regularity estimates developed by Armstrong and the author in (Comm. Pure Appl. Math. 71 (2018) 1717-1849); and a nonlinear concentration inequality of the Efron-Stein type which is used to transfer quantitative information from the environment to the correctors.