Regularity results of the speed of biased random walks on Galton-Watson trees

2018/11/12 by Tokushige, Yuki
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1811.04849

Abstract

We prove that the speed of λ-biased random walks on a supercritical Galton-Watson tree without leaves is differentiable when λ∈(0,1), and give an expression of the derivative using a certain 2-dimensional Gaussian random variable. The proof heavily uses the renewal structure of Galton-Watson trees that was introduced by Lyons-Pemantle-Peres.

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• Differentiability of the speed of biased random walks on Galton-Watson trees
• Monotonicity of the speed for biased random walk on Galton-Watson tree
• Speed of the biased random walk on a Galton--Watson tree
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