Investigation of the end-to-end distance distribution function for random and self-avoiding walks in two and three dimensions

Monte Carlo simulations employing the pivot algorithm are used to generate random and self-avoiding walks on two- and three-dimensional lattices. The moments of the end-to-end distance distribution function are calculated from the resulting configurations. It is found that the moments and the shape of the vector distribution function are in excellent agreement with the scaling form derived by des Cloizeaux.