Scaling Properties of the Probability Distribution for Growth Sites

A growth model can be characterized by the set of probabilities {pi}iɛг that each site at a given time on the external perimeter Г becomes part of the aggregate. All quantities of interest both static and dynamic can be expressed in terms of the pi. Equations for the set of pi are given for DLA and other growth models using the electrostatic analogy of the dielectric breakdown model. Due to this electrostatic analogy the scaling properties of the probability distribution are related to those of the voltage distribution in a random resistor and random superconducting network at the percolation threshold. An infinite set of exponents is necessary to fully characterize the moments of the distribution which are related to the surface structure of the aggregate.