Limit set of branching random walks on hyperbolic groups

2020/07/27 by Sidoravicius, Vladas, Wang, Longmin, Xiang, Kainan · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.13267

Abstract

Let Γ be a nonelementary hyperbolic group with a word metric d and ∂Γ its hyperbolic boundary equipped with a visual metric d_a for some parameter a>1. Fix a superexponential symmetric probability μ on Γ whose support generates Γ as a semigroup, and denote by ρ the spectral radius of the random walk Y on Γ with step distribution μ. Let ν be a probability on \1, 2, 3, …\ with mean λ=∑_k=1^∞ kν(k)

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