Quantitative stochastic homogenization for random conductance models with stable-like jumps

• 成果类型: Article
• 署名作者: Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
• 署名单位: Shanghai Jiao Tong University; University of Washington; University of Washington Seattle; Waseda University; Fujian Normal University; Fujian Normal University; Fujian Normal University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01354-5
• 发表日期: 2025
• 页码: 627-669
• 关键词: dirichlet problem; random-walks; REGULARITY; approximation; EQUATIONS; bounds

摘要

We consider random conductance models with long range jumps on Z(d), where the one-step transition probability from x to y is proportional to w( x,y) | x - y | (-d-alpha )with alpha is an element of ( 0 , 2). Assume that {w x,y } (x,y)is an element of E are independent, identically distributed and uniformly bounded non-negative random variables with E w(x,y) = 1, where E is the set of all unordered pairs on Z(d). We obtain a quantitative version of stochastic homogenization for these random walks, with explicit polynomial rates up to logarithmic corrections.