Statistics of equally weighted random paths on a class of selfsimilar 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 les b < infin). The obtained exact results on the first eight members of this family reveal that, for every b > 2, mean path endtoend 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2004
 DOI:
 10.1088/03054470/37/1/001
 arXiv:
 arXiv:mathph/0408055
 Bibcode:
 2004JPhA...37....1K
 Keywords:

 Random walksfractalsrenormalization;
 Mathematical Physics;
 Optics;
 31XX;
 32XX;
 35XX;
 44XX;
 78XX
 EPrint:
 20 pages, 2 figures