Speed of the biased random walk on a Galton--Watson tree

Abstract

We give an expression of the speed of the biased random walk on a Galton--Watson tree. In the particular case of the simple random walk, we recover the result of Lyons, Pemantle and Peres \cite{LyPePe95}. The proof uses a description of the invariant distribution of the environment seen from the particle.

reference added; Statement of Theorem 4.1 changed

Cited by in corpus (3)

• The maximal potential energy of biased random walks on trees
• A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases
• The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias