Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions

By Jim Pitman, Matthias Winkel. 2008

48 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8a2ade73693360ae8e0f53f07c54b783dbd7d6d0

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In Artificial Intelligence

In Condensed Matter Physics

In Mathematical Physics

Citations in the corpus

Scaling limits of Markov branching trees with applications to Galton–Watson and random unordered trees (2010, background): “4 Further non-consistent cases: (α, θ)-trees Another application concerns a family of binary labeled trees introduced by Pitman and Winkel [32] and built inductively according to a growth rule depending on two parameters α ∈ (0, 1) and θ ≥ 0.”
A new family of Markov branching trees: the alpha-gamma model (2008, unknown): “Lemma 8 (Theorem 3.8 in [22]) .”