Minimum growth probability of diffusion-limited aggregates

We calculate the minimum growth probability for diffusion-limited aggregation (DLA) as a function of the cluster mass M, and find a novel singularity of the form -ln${\mathit{p}}_{\min }$(M)∼(lnM${)}^{\mathit{y}}$ with y≊2. We interpret this result in terms of a simple model for DLA structure, which is characterized by a hierarchy of self-similar voids separated by channels whose diameter increases slower than the cluster diameter.