``Generalized des Cloizeaux'' exponent for self-avoiding walks on the incipient percolation cluster

We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function <P_B(r,N)> for the end-to-end distance r of an N step SAW behaves as a power law for r-->0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested ``generalized des Cloizeaux'' expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions.