These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …

These notes cover one of the topics programmed for the St Petersburg School in Probability
and Statistical Physics of June 2012. The aim is to review recent mathematical …

We consider a biased random walk X n on a Galton–Watson tree with leaves in the sub-
ballistic regime. We prove that there exists an explicit constant γ= γ (β)∈(0, 1), depending on …

We are interested in the biased random walk on a supercritical Galton–Watson tree in the
sense of Lyons (Ann. Probab. 18: 931–958, 1990) and Lyons, Pemantle and Peres (Probab …

Abstract Models of random walks in a random environment were introduced at first by
Chernoff in 1967 in order to study biological mechanisms. The original model has been …

We are interested in the randomly biased random walk on the supercritical Galton–Watson
tree. Our attention is focused on a slow regime when the biased random walk (X_n) is null …

We consider a continuous-time vertex reinforced jump process on a supercritical Galton–
Watson tree. This process takes values in the set of vertices of the tree and jumps to a …

We investigate the range $\mathcal {R} _T $ of the diffusive biased walk $\mathbb {X} $ on a
Galton-Watson tree $\mathbb {T} $ in random environment, that is to say the sub-tree of …

Consider a class of null-recurrent randomly biased walks on a supercritical Galton–Watson
tree. We obtain the scaling limits of the local times and the quenched local probability for the …

As a model of trapping by biased motion in random structure, we study the time taken for a
biased random walk to return to the root of a subcritical Galton‐Watson tree. We do so for …