EXPONENTIAL DECAY FOR SUBCRITICAL CONTACT AND PERCOLATION PROCESSES

• 成果类型: Article
• 署名作者: BEZUIDENHOUT, C; GRIMMETT, G
• 署名单位: University of Bristol
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990332
• 发表日期: 1991
• 页码: 984-1009
• 关键词: INEQUALITIES; models

摘要

We study the contact process, together with a version of the percolation process with one continuously varying coordinate. It is proved here that the radius of the infected cluster has an exponentially decaying tail throughout the subcritical phase. The same is true of the Lebesgue measure (in space-time) of this cluster. Certain critical-exponent inequalities are derived and the critical point of the percolation process in two dimensions is determined exactly.