High-Dimensional Diffusive Growth

Abstract

We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits a phase transition between ballistic and diffusion-controlled growth, with non-trivial corrections to cluster size at the critical point. Even in the ballistic regime, cluster scaling is controlled by extremal statistics due to the branching structure of the Cayley tree; it is the extremal nature of the fluctuations that enables us to solve the model.