Distribution of growth probabilities for off-lattice diffusion-limited aggregation

We study the distribution n(,M) of growth probabilities {pi} for off-lattice diffusion-limited aggregation (DLA) for cluster sizes up to mass M=20 000, where i==-pi/logM. We find that for large , log n(,M)-/logM, with =20.3 and =1.30.3. One consequence of this form is that the minimum growth probability pmin(M) obeys the asymptotic relation logpmin(M)-(logM)(+1+)/. We find evidence for the existence of a well-defined crossover value * such that only the rare configurations of DLA contribute to n(,M) for >*, while both rare and typical DLA configurations contribute for <*.