article · 2008
Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions
Pitman, Matthias Winkel
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Abstract
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. 1. Introduction. We
Cite this paper
Pitman, & Winkel, M. (2008). Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions.
Pitman, , and Matthias Winkel. “Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions.” 2008.
Pitman, and Matthias Winkel. 2008. “Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions.”
Pitman and Winkel, M. (2008) ‘Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions’.
@article{pitman2008regenerative,
title = {{Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions}},
author = {Pitman and Winkel, Matthias},
year = {2008}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.