The Einstein relation for finitely ramified Sierpinski carpets

Based on an analogy consideration between random walks and resistor network s it is shown that for a wide class of random walks on graphs resulting fro m finitely ramified Sierpinski carpets the Einstein relation is satisfied, which is an important equation relating conductivity and diffusivity. On fr actal graphs this relation means, for instance, that a wide class of random walk algorithms including the blind and myopic ant random walks have the s ame random walk dimension.