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

Details 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

2008-03-20

arxiv.org/abs/0803.3098v3

Annals of Probability 2009, Vol. 37, No. 5, 1999-2041

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AOP445 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/08-AOP445

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.

Affiliated with

Also associated with

No associations

Rating

Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586961