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 consider a system of particles which perform branching Brownian motion with negative
drift and are killed upon reaching zero, in the near-critical regime where the total population …

We consider branching Brownian motion on the real line with the following selection
mechanism: every time the number of particles exceeds a (large) given number N, only the …

We consider one-dimensional branching Brownian motion in which particles are absorbed
at the origin. We assume that when a particle branches, the offspring distribution is …

We study branching diffusions in a bounded domain D of R^ d R d in which particles are
killed upon hitting the boundary ∂ D∂ D. It is known that any such process undergoes a …

We consider a branching Brownian motion with linear drift in which particles are killed on
exiting the interval (0,K) and study the evolution of the process on the event of survival as the …

We consider branching Brownian motion on the real line with absorption at zero, in which
particles move according to independent Brownian motions with the critical drift of-2-2 …

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 …

The Fisher-Kolmogorov, Petrovski, Piscounov equation (FKPP) is a deterministic partial
differential equation. It describes the evolution of an invasion front from a stable phase into …

We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic
behavior of the survival probability of the branching random walk killed below a linear …