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

Dongjian Qian; Yang Xiao

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arXiv · 2405.11845

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

Dongjian Qian·Yang Xiao

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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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Dongjian Qian, Yang Xiao. 2024-05-20. Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree. https://arxiv.org/abs/2405.11845

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