We report results of Monte Carlo simulations of diffusion on random two-dimensional substrates generated by N-step random walks. In contrast to a previous study by Dekeyser, Maritan, and Stella [Phys. Rev. Lett. 58, 1758 (1987); Phys. Rev. A 36, 2338 (1987)], we find the effective exponent ${\nu }_{\mathrm{eff}}$ for the mean-square displacement of the diffusion process to be a slowly varying function of N, with (1/2-${\nu }_{\mathrm{eff}\mathrm{\propto }1/\mathrm{n}\mathit{N}}$ as N→∞.

• Received 28 October 1988

DOI:https://doi.org/10.1103/PhysRevA.39.4337