THE MAXIMAL FLOW FROM A COMPACT CONVEX SUBSET TO INFINITY IN FIRST PASSAGE PERCOLATION ON Zd

• 成果类型: Article
• 署名作者: Dembin, Barbara
• 署名单位: Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1367
• 发表日期: 2020
• 页码: 622-645
• 关键词: large deviations

摘要

We consider the standard first passage percolation model on Z(d) with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex subset A of R-d and infinity. The study of maximal flow is associated with the study of sets of edges of minimal capacity that cut A from infinity. We prove that the rescaled maximal flow between nA and infinity phi(nA)/n(d-1) almost surely converges toward a deterministic constant depending on A. This constant corresponds to the capacity of the boundary partial derivative A of A and is the integral of a deterministic function over. A. This result was shown in dimension 2 and conjectured for higher dimensions by Garet in (Annals of Applied Probability 19 (2009) 641-660).