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Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree

Probability 2024-05-21 v1

Abstract

This paper deals with a transient random walk in Dirichlet environment, or equivalently a linearly edge reinforced random walk, on a Galton-Watson tree. We compute the stationary distribution of the environment seen from the particle of an edge reinforced random walk. We obtain a formula for the speed and give a necessary and sufficient condition for the walk to have a positive speed under some moment conditions on the offspring distribution of the tree.

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Cite

@article{arxiv.2405.11845,
  title  = {Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree},
  author = {Dongjian Qian and Yang Xiao},
  journal= {arXiv preprint arXiv:2405.11845},
  year   = {2024}
}