THE SURVIVAL OF LARGE DIMENSIONAL THRESHOLD CONTACT PROCESSES

• 成果类型: Article
• 署名作者: Mountford, Thomas; Schonmann, Roberto H.
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of California System; University of California Los Angeles
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP440
• 发表日期: 2009
• 页码: 1483-1501
• 关键词: population-growth model; sexual reproduction; STABILITY

摘要

We study the threshold theta contact process on Z(d) with infection parameter lambda. We show that the critical point lambda(c), defined as the threshold for survival starting from every site occupied, vanishes as d -> infinity. This implies that the threshold theta voter model on Z(d) has a nondegenerate extremal invariant measure, when d is large.