Cluster Shape and Critical Exponents near Percolation Threshold

The shape of the large, random clusters, occurring near percolation threshold c₀, is shown to be such that the mean cluster boundary-to-bulk ratio 〈b〉〈n〉 gives c₀. A Monte Carlo calculation yields that the cluster size distribution is proportional to a Gaussian in bn which is independent of concentration and narrows to a function as n; the asymptotic behavior gives c₀ and the critical exponents.