Distribution of dangling ends on the incipient percolation cluster

We study numerically and by scaling arguments the probability P(M)dM that a given dangling end of the incipient percolation cluster has a mass between M and M+dM. We find by scaling arguments that P(IM) decays with a power la w, P(M)similar to M-(1+kappa), With an exponent kappa = d(f)(B)/d(f), Where d(f) and d(f)(B) are the fractal dimensions of the cluster and its backbon e, respectively. Our numerical results yield kappa = 0.83 in d = 2 and kapp a = 0.74 in d = 3 in very good agreement with theory. (C) 1999 Published by Elsevier Science B.V. All rights reserved.