250 research outputs found
Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions
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.Comment: Published in at http://dx.doi.org/10.1214/08-AOP445 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Moments of convex distribution functions and completely alternating sequences
We solve the moment problem for convex distribution functions on in
terms of completely alternating sequences. This complements a recent solution
of this problem by Diaconis and Freedman, and relates this work to the
L\'{e}vy-Khintchine formula for the Laplace transform of a subordinator, and to
regenerative composition structures.Comment: Published in at http://dx.doi.org/10.1214/193940307000000374 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
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