Journal of Statistical Physics, Vol. 102, Nos. 12, 2001. p. 97-113.
These results explore the asymptotic behavior of the density of a system of coalescing random walks where particles begin from only a subspace of the integer lattice and are allowed to walk anywhere on the lattice. They generalize results by Bramson and Griffeath from 1980. Since the probability that a given site is occupied depends on how far that site is from the originating sub-space, the density of the system at a given time must be re-defined. However, the general idea is still that if the density is larger than we expect at a given time, more coalescing events will occur, and the density will correct itself over time.