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.
Publié le : 2009-09-15
Classification:
Regenerative composition,
Poisson–Dirichlet composition,
Chinese Restaurant Process,
Markov branching model,
self-similar fragmentation,
continuum random tree,
ℝ-tree,
recursive random tree,
phylogenetic tree,
60J80
@article{1253539862,
author = {Pitman, Jim and Winkel, Matthias},
title = {Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 1999-2041},
language = {en},
url = {http://dml.mathdoc.fr/item/1253539862}
}
Pitman, Jim; Winkel, Matthias. Regenerative tree growth: Binary self-similar continuum random trees and Poisson–Dirichlet compositions. Ann. Probab., Tome 37 (2009) no. 1, pp. 1999-2041. http://gdmltest.u-ga.fr/item/1253539862/