Diffusion on two-dimensional random walks

Analysis of Monte Carlo enumerations for diffusion on the fractal structure generated by the random walk on a two-dimensional lattice allows us to predict a behavior 〈r〉∼${\mathrm{n}}^{\nu }$(lnn${)}^{\mathrm{\alpha }}$ with ν=0.325±0.01 and α=0.35±0.03. This leads to the conjecture that ν=α=(1/3). This value of ν, and the presence of logarithmic corrections, are strongly supported by heuristic arguments based on Flory theory and on plausible assumptions. Evidence for the validity of these assumptions and the Flory approach is coming from remarkably successful applications in related problems.