Surface structure of random aggregates on the Cayley tree

Abstract

Growth through ballistic aggregation and biased diffusion-limited aggregation is investigated on the Cayley tree. For a general branching ratio it is shown that the surface width of a ballistic aggregate remains finite (of order one) as the cluster mass goes to infinity. DLA with an attractive bias is treated approximately. For non-zero bias strength the surface width is asymptotically finite. In the limit of isotropic diffusion (zero bias) a roughening transition occurs which can be described in terms of a single diverging length scale.