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 …

Consider the following interacting particle system on the d-ary tree, known as the frog model:
Initially, one particle is awake at the root and iid Poisson many particles are sleeping at …

We study a branching random walk on R with an absorbing barrier. The position of the
barrier depends on the generation. In each generation, only the individuals born below the …

Let M_n be the minimal position in the n th generation, of a real-valued branching random
walk in the boundary case. As n→∞, M_n-32\logn is tight (see (Ann. Probab. 37 (2009) …

We consider a branching random walk on R starting from x≥ 0 and with a killing barrier at 0.
At each step, particles give birth to b children, which move independently. Particles that …

In this thesis, branching Brownian motion (BBM) is a random particle system where the
particles diffuse on the real line according to Brownian motions and branch at constant rate …

We are interested in predator–prey dynamics on infinite trees, which can informally be seen
as particular two-type branching processes where individuals may die (or be infected) only …

We consider the slow movement of randomly biased random walk (X_n) on a supercritical
Galton-Watson tree, and are interested in the sites on the tree that are most visited by the …

We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This
model was defined as the chase-escape model by Kordzakhia and it admits a limit process …

We consider a large family of branching-selection particle systems. The branching rate of
each particle depends on its rank and is given by a function b defined on the unit interval …