Statistics of equally weighted random paths on a class of self-similar structures

We study the statistics of equally weighted random walk paths on a family of Sierpinski gasket lattices whose members are labelled by an integer b (2 ? b 2, mean path end-to-end distance grows more slowly than any power of its length N. We provide arguments for the emergence of usual power law critical behaviour in the limit b ? ? when fractal lattices become almost compact.

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