GROWTH PROBABILITY-DISTRIBUTION IN PERCOLATION

We study the growth probability distribution for a single cluster growth process for percolation at the percolation threshold. We find that this distribution is indistinguishable from the chemical path distribution on the percolation cluster as studied by Havlin et al. We also study the density profile of the percolation cluster. Using the multiscaling idea of Coniglio and Zannetti we calculate the fractal dimension of the percolation clusters from the density profile and report d(f) = 1.895 +/- 0.005 for two dimensions and 2.50 +/- 0.01 for three dimensions. However we do not find any evidence of multifractal or multiscaling behaviour.