The survival of nonattractive interacting particle systems on Z

• 成果类型: Article
• 署名作者: Sudbury, A
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160329
• 发表日期: 2000
• 页码: 1149-1161
• 关键词: Bounds

摘要

We consider interacting particle systems on Z which allow five types of pairwise interaction: Annihilation, Birth, Coalescence, Death and Exclusion with corresponding rates a, b, c, d, e. We show that whatever the values of a, c, d, e, if the birthrate is high enough there is a positive probability the particle system will survive starting from airy finite occupied set. In particular: an IFS with rates a, b, c, d, e has a positive probability of survival if b > 4d + 6a, c + a greater than or equal to d + e, or b > 7d + 3a - 3c + 3e, c + a < d + e. We create a suitable supermartingale by extending the method used by Holley and Liggett in their treatment of the contact process.