English

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).

Keywords

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)

R2 v1 2026-06-21T16:57:18.364Z