Shapes of generalized random walks

Shape parameters for self-avoiding, random, and collapsed walks have been determined analytically and numerically using the results of recent work on the path integral description of generalized Brownian motion. The analytical calculations are both simple and exact, and the predicted values of the shape parameters in two and three dimensions are in close agreement with the simulation results and with the available literature data, which are generally obtained by approximate, non-trivial perturbation approaches. Typical realizations of actual walks in two dimensions suggest that despite its nonstationary character, the underlying generalized random walk process can serve as a useful minimal model of chain configurations.