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 les b < infin). 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 rarr infin when fractal lattices become almost compact.
Journal of Physics A Mathematical General
- Pub Date:
- January 2004
- Random walksfractalsrenormalization;
- Mathematical Physics;
- 20 pages, 2 figures