Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions
نویسندگان
چکیده
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 twoparameter 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.
منابع مشابه
Regenerative Tree Growth: Binary Self-similar Continuum Random Trees and Poisson–dirichlet Compositions1 by Jim Pitman
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 t...
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