  We consider an interacting particle system on the one dimensional lattice
$\bf Z$ modeling combustion. The process depends on two integer parameters
$2\le a<M<\infty$. Particles move independently as continuous time simple
symmetric random walks except that 1. When a particle jumps to a site which has
not been previously visited by any particle, it branches into $a$ particles; 2.
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 $r_t$, 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.
