The Annals of Applied Probability

Poisson–Dirichlet branching random walks

Louigi Addario-Berry and Kevin Ford

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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 $(v_{1},v_{2},\ldots)$, where each $v_{j}$ is the sum of $j$ independent $\operatorname{Exponential}(1)$ 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 $O(1)$.

Article information

Ann. Appl. Probab., Volume 23, Number 1 (2013), 283-307.

First available in Project Euclid: 25 January 2013

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Branching random walk random recursive tree Pratt tree heights of trees


Addario-Berry, Louigi; Ford, Kevin. Poisson–Dirichlet branching random walks. Ann. Appl. Probab. 23 (2013), no. 1, 283--307. doi:10.1214/12-AAP840.

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