THE NUMBER OF OPEN PATHS IN ORIENTED PERCOLATION

• 成果类型: Article
• 署名作者: Garet, Olivier; Gouere, Jean-Baptiste; Marchand, Regine
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Tours; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1158
• 发表日期: 2017
• 页码: 4071-4100
• 关键词: random environment; contact process; GROWTH

摘要

We study the number N-n of open paths of length n in supercritical oriented percolation on Z(d) x N, with d >= 1, and we prove the existence of the connective constant for the supercritical oriented percolation cluster: on the percolation event {inf N-n > 0}, N-n(1/n) almost surely converges to a positive deterministic constant. The proof relies on the introduction of adapted sequences of regenerating times, on subadditive arguments and on the properties of the coupled zone in supercritical oriented percolation. This global convergence result can be deepened to give directional limits and can be extended to more general random linear recursion equations known as linear stochastic evolutions.