Poisson--Dirichlet branching random walks

Details Poisson--Dirichlet branching random walks Poisson--Dirichlet branching random walks

2010-12-12

arxiv.org/abs/1012.2544v2

Mathematics

Probability

20 pages, 1 figure; minor revisions

Scientific paper

We determine, to within O(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (v_1,v_2,...) where each v_j is the sum of j independent Exponential(1) random variables and the different v_i need not be independent. In particular, our analysis applies to the Poisson-Dirichlet branching random walk and to the Poisson-weighted infinite tree. As a corollary, we also determine the expected height of a random recursive tree to within O(1).

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