LARGE-SCALE REGULARITY IN STOCHASTIC HOMOGENIZATION WITH DIVERGENCE-FREE DRIFT

• 成果类型: Article
• 署名作者: Fehrman, Benjamin
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1872
• 发表日期: 2023
• 页码: 2559-2599
• 关键词: CENTRAL-LIMIT-THEOREM; random-walks; invariance-principle; isotropic diffusions; Liouville theorem; compactness methods; elliptic-equations; time; percolation; stationary

摘要

We provide a proof of stochastic homogenization for random environ-ments with a mean zero, divergence-free drift. We prove that the environ-ment homogenizes weakly in H1 if the drift admits a stationary L2-integrable stream matrix, and we prove that the two-scale expansion converges strongly in H1 if the drift admits a stationary Ld & PROVES;(2+& delta; )-integrable stream matrix. Ad-ditionally, under this stronger integrability assumption, we show that the en-vironment almost surely satisfies a large-scale Holder regularity estimate and first-order Liouville principle.