When two identical diffusing and absorbing particles are placed in 1d space, their survival probability S(T) is a well known function of the dimensionless time T=(Dt)/(xo)^2, (where D is the sum of the diffusion constants of the two particles, t is the dimensional time, and xo is the initial separation of the two particles). This survival probability for 2-particle coalescence in 1d (where the coalescence reaction is A+A->A) is Erf[1/(4T)^0.5], which scales a sT^(-0.5) in the long-time limit. (Erf is the error function).

To find the survival probability for 3-particle coalescence in 1d,

the Fisher-Gelfand (1988) approach should be used in which the

three particles are treated as a single composite particle that is absorbed when it touches either of the two plane surfaces of a wedge opening. From that approach, the survival probability is seen to scale as T^(-1.5) in the long-time limit, indicating faster kinetics for the 3-particle coalescence reaction.

When the coalescence of many particles in 1d is considered, in which all of the particles have the same initial spacing from each other, (which was done by Ben-Avraham in 1990), the survival probability is found to be the same as for 2-particle coalescence, which once again scales as T^(-0.5) in the long time limit.

Why, conceptually, is there a return to slower kinetics as the number of coalescing particles in 1d increases? Shouldn't the coalescence kinetics become faster and faster in 1d as more and more particles are added to the system? Any answers to this question would be greatly appreciated.