GROWTH PROBABILITY-DISTRIBUTION AND MOMENTS OF LOG-PROBABILITY IN DIFFUSION-LIMITED AGGREGATION

Abstract

We reconsider the growth probability distribution in diffusion limited aggregation. By comparing the analytic solution of the growth probability distribution for a hierarchical model with numerical data of Monte Carlo simulations, we present a new functional form describing the tail behavior of the growth probability distribution. In addition, we study a finite-mass dependent behavior of moments of logarithm of the growth probability and a moment dependent behavior of its amplitude. It is found that the q-th moment, mu(q), of logarithm of the growth probability exhibits unifractal behavior with respect to 1nM as mu(q) similar to B-q(lnM)(q) for all q. Also the amplitude B-q behaves as lnB(q) similar to q for all q in the limit of M-->infinity.