A functional limit theorem for the profile of $b$-ary trees
Probability
2010-10-18 v1
Abstract
In this paper we prove a functional limit theorem for the weighted profile of a -ary tree. For the proof we use classical martingales connected to branching Markov processes and a generalized version of the profile-polynomial martingale. By embedding, choosing weights and a branch factor in a right way, we finally rediscover the profiles of some well-known discrete time trees.
Cite
@article{arxiv.1010.3092,
title = {A functional limit theorem for the profile of $b$-ary trees},
author = {Eva-Maria Schopp},
journal= {arXiv preprint arXiv:1010.3092},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AAP640 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)