Scaling for random walks on Eden trees

Random walks are simulated on finite stages of construction of Eden trees in dimensions D=2 and 3, and it is shown that the mean-square displacement [R(N)(2)], of N-step walks and the mean number of distinct visited sites [S-N] obey finite-size scaling. Accurate estimates of the dimensions of the random walks D-w, are obtained and the relation [S-N]similar to N-DIDw/(logN)(alpha) is shown to hold in these fractals, with positive exponents alpha. Then the Alexander-Orbach scaling relation D-s=2D/D-w is satisfied, where D-s is the spectral dimension, contrary to previous proposals in these and other treelike structures.