The speed of a biased random walk on a Galton-Watson tree is analytic
Adam Bowditch, Yuki Tokushige
TL;DR
This paper proves that the speed of a biased random walk on a supercritical Galton-Watson tree is an analytic function within the ballistic regime, extending previous differentiability results.
Contribution
It establishes the analyticity of the speed in the ballistic regime, advancing understanding of random walks on Galton-Watson trees.
Findings
Speed is analytic within the ballistic regime.
Extends previous differentiability results.
Provides new insights into the behavior of biased random walks.
Abstract
We prove that the speed of a biased random walk on a supercritical Galton-Watson tree conditioned to survive is analytic within the ballistic regime. This extends the previous work arXiv:1906.07913 in which it was shown that the speed is differentiable within the range of bias for which a central limit theorem holds.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods