Poisson-Dirichlet branching random walks

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).

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)

References in corpus (3)

• Convergence in law of the minimum of a branching random walk
• Minima in branching random walks
• Tightness for a family of recursion equations

Cited by in corpus (4)

• Continuum Cascade Model: Branching Random Walk for Traveling Wave
• Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models
• Prime chains and Pratt trees
• Euclidean Embedding of the Poisson Weighted Infinite Tree and Application to Mobility Models