A tale of two balloons

• 成果类型: Article
• 署名作者: Angel, Omer; Ray, Gourab; Spinka, Yinon
• 署名单位: University of British Columbia; University of Victoria; Tel Aviv University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01165-6
• 发表日期: 2023
• 页码: 815-837
• 关键词: independent sets; regular graphs

摘要

From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the hyperbolic plane and regular trees. The result for the Euclidean space relies on a novel 0-1 law for stationary processes. Towards establishing the results for the hyperbolic plane and regular trees, we prove an upper bound on the density of any well-separated set in a regular tree which is a factor of an i.i.d. process.