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arXiv · 1906.07913

Differentiability of the speed of biased random walks on Galton-Watson trees

Adam Bowditch·Yuki Tokushige
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Abstract

We prove that the speed of a $\lambda$-biased random walk on a supercritical Galton-Watson tree is differentiable for $\lambda$ such that the walk is ballistic and obeys a central limit theorem, 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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Adam Bowditch, Yuki Tokushige. 2019-06-19. Differentiability of the speed of biased random walks on Galton-Watson trees. https://arxiv.org/abs/1906.07913

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