REGENERATIVE TREE GROWTH: BINARY SELF-SIMILAR CONTINUUM RANDOM TREES AND POISSON-DIRICHLET COMPOSITIONS

• 成果类型: Article
• 署名作者: Pitman, Jim; Winkel, Matthias
• 署名单位: 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-AOP445
• 发表日期: 2009
• 页码: 1999-2041
• 关键词: fragmentations

摘要

We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of Ford's trees. In general, the Markov branching trees induced by the two-parameter growth rule are not sampling consistent, so the existence of compact limiting trees cannot be deduced from previous work on the sampling consistent case. We develop here a new approach to establish such limits, based on regenerative interval partitions and the urnmodel description of sampling from Dirichlet random distributions.