Weak convergence for the minimal position in a branching random walk: a simple proof

Z. Shi (1) , E. Aïdekon

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Consider the boundary case in a one-dimensional super-critical branching random walk. It is known that upon the survival of the system, the minimal position after n steps behaves in probability like 3/2 log n when n -> infinity. We give a simple and self-contained proof of this result, based exclusively on elementary properties of sums of i.i.d. real-valued random variables.

Domaines: Probabilités [math.PR]

Z. Shi, E. Aïdekon. Weak convergence for the minimal position in a branching random walk: a simple proof. Periodica Mathematica Hungarica, 2010, 61 (1-2), pp.43-54. ⟨10.1007/s10998-010-3043-x⟩. ⟨hal-00707219⟩