Mh. Kim et al., LOWER AND UPPER-BOUNDS FOR THE ANOMALOUS DIFFUSION EXPONENT ON SIERPINSKI CARPETS, Journal of physics. A, mathematical and general, 26(21), 1993, pp. 5655-5660
The anomalous diffusion exponent d(W) of random walks on a family of S
ierpinski carpets are studied by analytical and numerical methods. We
construct an effective bulk resistor and then establish the lower and
upper bounds for d(W), where the lower bound turns out to be the same
as that obtained with bond-moving renormalization. Numerical simulatio
ns on a family of Sierpinski carpets confirm our bounds, and show stro
ng dependence of d(W) on the lacunarity of the carpet.