Journal of Statistical Physics, Vol. 52, Nos. 1/2, 1988. p. 203-236.
We study numerically and by scaling methods the distributions and moments of several structural properties of percolation clusters in two and three dimensions. The clusters are generated at criticality and properties such as the distribution of the mass as a function of linear size or chemical distance are studied. Our results suggest that the hierarchy of moments can be represented by a single gap exponent. Using a scaling approach, we obtain analytical forms for the different distribution functions which agree very well with the numerical data.