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arXiv · 1505.04949

The maximum of a tree-indexed random walk in the big jump domain

Pascal Maillard
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Abstract

We consider random walks indexed by arbitrary finite random or deterministic trees. We derive a simple sufficient criterion which ensures that the maximal displacement of the tree-indexed random walk is determined by a single large jump. This criterion is given in terms of four quantities : the tail and the expectation of the random walk steps, the height of the tree and the number of its vertices. The results are applied to critical Galton--Watson trees with offspring distributions in the domain of attraction of a stable law.

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Pascal Maillard. 2016-06-13. The maximum of a tree-indexed random walk in the big jump domain. https://arxiv.org/abs/1505.04949

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