POISSON SPLITTING BY FACTORS

• 成果类型: Article
• 署名作者: Holroyd, Alexander E.; Lyons, Russell; Soo, Terry
• 署名单位: Microsoft; Indiana University System; Indiana University Bloomington; University of Victoria
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP651
• 发表日期: 2011
• 页码: 1938-1982
• 关键词: matchings; entropy; trees

摘要

Given a homogeneous Poisson process on R-d with intensity lambda, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that each set of points forms a homogeneous Poisson process, with any given pair of intensities summing to lambda. In particular, this answers a question of Ball [Electron. Commun. Probab. 10 (2005) 60-69], who proved that in d = 1, the Poisson points may be similarly partitioned (via a translation-equivariant function) so that one set forms a Poisson process of lower intensity, and asked whether the same is possible for all d. We do not know whether it is possible similarly to add points (again chosen as a deterministic function of a Poisson process) to obtain a Poisson process of higher intensity, but we prove that this is not possible under an additional finitariness condition.