5 Sharp phase transition in the random stirring model on trees

• 成果类型: Article
• 署名作者: Hammond, Alan
• 署名单位: University of Oxford
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0543-7
• 发表日期: 2015
• 页码: 429-448
• 关键词: cycles

摘要

We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists such that, for any , the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree almost surely contains an infinite cycle consists of a semi-infinite interval. The critical point at the left-hand end of this interval is at least and at most .