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(M) decays with a power law, P(M) M−(1+κ), with an exponent κ=dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield κ=0.83 in d=2 and κ=0.74 in d=3 in very good agreement with theory.