AN ELLIPTIC HARNACK INEQUALITY FOR DIFFERENCE EQUATIONS WITH RANDOM BALANCED COEFFICIENTS

• 成果类型: Article
• 署名作者: Berger, Noam; Cohen, Moran; Deuschel, Jean-Dominique; Guo, Xiaoqin
• 署名单位: Technical University of Munich; Hebrew University of Jerusalem; Technical University of Berlin; University System of Ohio; University of Cincinnati
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1544
• 发表日期: 2022
• 页码: 835-873
• 关键词: quenched invariance-principle; Stochastic Homogenization; random-walks; REGULARITY

摘要

We prove an elliptic Harnack inequality at large scale on the lattice Z(d) for nonnegative solutions of a difference equation with balanced i.i.d. coefficients which are not necessarily elliptic. We also identify the optimal constant in the Harnack inequality. Our proof relies on a quantitative homogenization result of the corresponding invariance principle to Brownian motion and on percolation estimates. As a corollary of our main theorem, we derive an almost optimal Holder estimate.