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 …

Consider a transient random walk (Zn) on an infinite graph. As the time n tends to∞, Zn
escapes to infinity due to its transience. It is the aim of this thesis to study several problems …

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 …

We prove that the speed of $\lambda $-biased random walks on a supercritical Galton-
Watson tree without leaves is differentiable when $\lambda\in (0, 1) $, and give an …

Random Walks on random trees and hyperbolic groups: trace processes on boundaries at
infinity and the speed of biased random walks (ランダム木グラフと双曲群上のランダムウォーク …