The range of tree-indexed random walk
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Publication:2800012
DOI10.1017/S1474748014000280zbMATH Open1339.60049arXiv1307.5221MaRDI QIDQ2800012
Author name not available (Why is that?)
Publication date: 14 April 2016
Published in: (Search for Journal in Brave)
Abstract: We provide asymptotics for the range R(n) of a random walk on the d-dimensional lattice indexed by a random tree with n vertices. Using Kingman's subadditive ergodic theorem, we prove under general assumptions that R(n)/n converges to a constant, and we give conditions ensuring that the limiting constant is strictly positive. On the other hand, in dimension 4 and in the case of a symmetric random walk with exponential moments, we prove that R(n) grows like n/(log n). We apply our results to asymptotics for the range of branching random walk when the initial size of the population tends to infinity.
Full work available at URL: https://arxiv.org/abs/1307.5221
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