LOWER AND UPPER-BOUNDS FOR THE ANOMALOUS DIFFUSION EXPONENT ON SIERPINSKI CARPETS

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.