分野別セミナー

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. This talk is based on the joint work with Adam Bowditch (National University of Singapore).