The Spread of a Catalytic Branching Random Walk

Philippe Carmona (1) , Yueyun Hu (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We consider a random walk on $\Z$ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_n$. Then we determine all possible limiting law for the sequence $M_n -\alpha n$ where $\alpha$ is a deterministic constant.

Mots clés: Branching processes; catalytic branching random walk

Domaines: Probabilités [math.PR]

Philippe Carmona, Yueyun Hu. The Spread of a Catalytic Branching Random Walk. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2014, 50 (2), pp.327--351. ⟨hal-00665271v3⟩