Phys. Rev. E 54, R3079–R3081 (1996)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 〈RN2〉 of N-step walks and the mean number of distinct visited sites 〈SN〉 obey finite-size scaling. Accurate estimates of the dimensions of the random walks Dw are obtained and the relation 〈SN〉∼ND/Dw/(logN)α is shown to hold in these fractals, with positive exponents α. Then the Alexander-Orbach scaling relation Ds=2D/Dw is satisfied, where Ds is the spectral dimension, contrary to previous proposals in these and other treelike structures. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.54.R3079
DOI:
10.1103/PhysRevE.54.R3079
PACS:
05.40.+j, 05.50.+q
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