Cluster persistence in one-dimensional diffusion-limited cluster-cluster aggregation

The persistence probability, P _C(t), of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size s as D(s)∼s^γ. In the mean field the problem maps to the survival of three annihilating random walkers with time-dependent noise correlations. For γ≥0 the motion of persistent clusters becomes asymptotically irrelevant and the mean-field theory provides a correct description. For γ<0 the spatial fluctuations remain relevant and the persistence probability is over-estimated by the random walk theory. The decay of persistence determines the small size tail of the cluster size distribution. For 0<γ<2 the distribution is flat and, surprisingly, independent of γ.