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arXiv · 1012.2544

Poisson-Dirichlet branching random walks

Louigi Addario-Berry·Kevin Ford
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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).

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Louigi Addario-Berry, Kevin Ford. 2010-12-12. Poisson-Dirichlet branching random walks. https://doi.org/10.1214/12-aap840

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