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

Abstract

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 < ∞). The obtained exact results on the first eight members of this family reveal that, for every 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.