2019/06/19 by Adam Bowditch, Bowditch, Adam, Yuki Tokushige +1
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1906.07913
We prove that the speed of a λ-biased random walk on a supercritical Galton-Watson tree is differentiable for λ 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.