Poisson-Dirichlet branching random walks
Probability
2013-02-13 v3
Abstract
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).
Cite
@article{arxiv.1012.2544,
title = {Poisson-Dirichlet branching random walks},
author = {Louigi Addario-Berry and Kevin Ford},
journal= {arXiv preprint arXiv:1012.2544},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AAP840 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)