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

2024/05/20 by Dongjian Qian, Yang Xiao, Qian, Dongjian +1
Mathematics · Physics and Astronomy · #60F15 #60J80 #60K35 #60K37 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2405.11845

openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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