A functional limit theorem for the profile of $b$-ary trees

Abstract

In this paper we prove a functional limit theorem for the weighted profile of a $b$-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.

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)

References in corpus (4)

• A functional limit theorem for the profile of search trees
• Discretization methods for homogeneous fragmentations
• Width and mode of the profile for some random trees of logarithmic height
• On the Height Profile of a Conditioned Galton-Watson Tree