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

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

2010-10-15

arxiv.org/abs/1010.3092v1

Annals of Applied Probability 2010, Vol. 20, No. 3, 907-950

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP640 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP640

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.

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