The Spread of a Catalytic Branching Random Walk

Abstract

We consider a random walk on $\mathbb{Z}$ 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.

arXiv comment34 pages, submitted