Exact solutions for diffusion-reaction processes in one dimension. II. Spatial distributions

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Abstract
For pt.I see Phys. Rev. Lett., vol.60, p.871 (1988). The author examines one-dimensional diffusion-reaction processes. Exact results are given for one-dimensional polymerisation (cluster-cluster aggregation) occurring on subsets of Z, the infinite lattice, or R, the infinite line; the subsets may have periodic, absorbing or reflecting boundary conditions. Part I. gave spatially averaged polymer concentrations; this paper describes the spatial distribution of the concentrations. His results have corollaries applying to coalescing random walks, and to binary and n-ary annihilation, since these are just polymerisation, modulos 1, 2 or n. Through well known dualities, his results also apply implicitly to the T=0 limit of the kinetic Ising model and to two interacting particle processes, the invasion and voter models.