The maximum of a tree-indexed random walk in the big jump domain
Probability
2018-06-20 v3
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.
Keywords
Cite
@article{arxiv.1505.04949,
title = {The maximum of a tree-indexed random walk in the big jump domain},
author = {Pascal Maillard},
journal= {arXiv preprint arXiv:1505.04949},
year = {2018}
}
Comments
17 pages. v2: added e-mail and grant number, no other changes v3: several small changes, changed the structure of the article (merged sections 4 and 5)