CAPACITIVE FLOWS ON A 2D RANDOM NET

• 成果类型: Article
• 署名作者: Garet, Olivier
• 署名单位: Universite de Lorraine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP556
• 发表日期: 2009
• 页码: 641-660
• 关键词: maximal flows; percolation; SURFACES; THEOREMS

摘要

This paper concerns maximal flows on Z(2) traveling from a convex set to infinity, the flows being restricted by a random capacity. For every compact convex set A, we prove that the maximal flow Phi(nA) between nA and infinity is such that Phi(nA)/n it almost surely converges to the integral of a deterministic function over the boundary of A. The limit can also be interpreted as the optimum of a deterministic continuous max-flow problem. We derive some properties of the infinite cluster in supercritical Bernoulli percolation.