The Spread of a Catalytic Branching Random Walk
  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. 
Philippe Carmona (LMJL), Yueyun Hu (LAGA)
math.PR