We consider a system of particles, each of which performs a continuous time random walk on Z. The particles interact only at times when a particle jumps to a site at which there are a number of other particles present. If there are j particles present, then the particle which just jumped is removed from the system with probability pj . We show that if pj is increasing in j and if the dimension d is at least 6 and if we start with one particle at each site of Z, then p(t) := P{there is at least… CONTINUE READING