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 b/n which is independent of concentration and narrows to a δ function as n→∞; the asymptotic behavior gives c₀ and the critical exponents.