Maximal displacement in a branching random walk through interfaces

Bastien Mallein (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains constant. We prove that the asymptotic behaviour of the maximal displacement in this process consists of a first ballistic order, given by the solution of an optimization problem under constraints, a negative logarithmic correction, plus stochastically bounded fluctuations.

Mots clés: Branching process; Branching random walk; random walk; time-inhomogeneous environment

Domaines: Probabilités [math.PR]

Bastien Mallein. Maximal displacement in a branching random walk through interfaces. Electronic Journal of Probability, 2015, ⟨10.1214/EJP.v20-2828⟩. ⟨hal-00826770⟩