Asymptotic density in a threshold coalescing and annihilating random walk (Q1872181)

The paper deals with an interacting random walk on \(Z^{d};\) the interaction is specified as follows: a particle jumps to a site only when there are at least \(n-1\) other particles present. Then the particle coalesces with probability \(c_{m}\) and annihilates (is removed from the system) with probability \(a_{m}\) where \(m\geq n-1\) is the number of particles present. The author shows that under certain conditions for \(n\geq 3,\) the probability that the origin is occupied at time \(t\) is a negative power law in \(t,\) the exponent being \(1/(n-1)\).