SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES

• 成果类型: Article
• 署名作者: Haas, Benedicte; Pitman, Jim; Winkel, Matthias
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of California System; University of California Berkeley; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP434
• 发表日期: 2009
• 页码: 1381-1411
• 关键词: self-similar fragmentations; stable subordinator; REPRESENTATION; asymptotics; mass; LAWS

摘要

We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees are the only ones whose distribution is invariant under uniform re-rooting.