Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions
Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions
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再生树生长：二元自相似连续随机树和泊松-狄利克雷组合
DOI：
10.1214/08-aop445
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Matthias Winkel
中科院分区：
文献类型：
--
作者：
J. Pitman;Matthias Winkel
我们使用一个自然有序的中国餐馆过程的扩展，生长一个双参数家庭的二进制自相似连续破碎树。我们提供了一个明确的嵌入福特的阿尔法模型树序列中的连续树，我们在以前的文章中确定为分布缩放限制的福特的树。一般情况下，由双参数增长规则导出的马尔可夫分枝树都不是采样一致的，因此不能从以前的工作中推导出紧极限树的存在性.我们在这里开发了一种新的方法来建立这样的限制，再生的间隔分区和瓮模型描述的Dirichlet随机分布的采样的基础上。
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 urn-model description of sampling from Dirichlet random distributions.