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_N²〉 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〉∼N^{D / D_w} / (logN)^α is shown to hold in these fractals, with positive exponents α. 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.