Fluctuations of the front in a stochastic combustion model

We consider an interacting particle system on the one-dimensional lattice Z modeling combustion. The process depends on two integer parameters 2?a?M<∞. Particles move independently as continuous time simple symmetric random walks except that (i) when a particle jumps to a site which has not been previously visited by any particle, it branches into a particles, (ii) when a particle jumps to a site with M particles, it is annihilated. We start from a configuration where all sites to the left of the origin have been previously visited and study the law of large numbers and central limit theorem for rt, the rightmost visited site at time t. The proofs are based on the construction of a renewal structure leading to a definition of regeneration times for which good tail estimates can be performed.