Poisson-Dirichlet branching random walks

Louigi Addario-Berry, Kevin Ford

Research output: Contribution to journalArticlepeer-review

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 (v1, v2, . . .), where each vj 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).

Original languageEnglish (US)
Pages (from-to)283-307
Number of pages25
JournalAnnals of Applied Probability
Volume23
Issue number1
DOIs
StatePublished - Feb 2013

Keywords

  • Branching random walk
  • Heights of trees
  • Pratt tree
  • Random recursive tree

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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