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 …

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 …

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 study supercritical branching Brownian motion on the real line starting at the origin and
with constant drift c. At the point x> 0, we add an absorbing barrier, ie individuals touching …

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 …

Consider a branching random walk on the real line with a killing barrier at zero: starting from
a nonnegative point, particles reproduce and move independently, but are killed when they …

We consider a branching random walk initiated by a single particle at location 0 0 in which
particles alternately reproduce according to the law of a Galton-Watson process and …

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 branching random walk for which the maximum position of a particle in the
n'th generation, R n, has zero speed on the linear scale: R n/n→ 0 as n→∞. We further …

We introduce a random barrier to a supercritical branching random walk in an iid random
environment $\{\mathcal {L} _n\} $ indexed by time $ n, $ ie, in each generation, only the …