Scaling exponents for random walks on Sierpinski carpets and number of distinct sites visited: a new algorithm for infinite fractal lattices

摘要

The scaling exponent for the mean square distance covered in a random walk (d_w) and the average number of distinct sites visited (d_n) are determined for a family of Sierpinski carpet patterns. We suggest a new random walk algorithm to generate walks on an effectively infinite deterministic fractal lattice. The algorithm is applied to several Sierpinski carpet patterns with the same Hausdorff dimension. We show that the systems have a quite different scaling exponent d_w and, further, that the generally accepted result d_n = d_s does not hold for all of these, where d_s is the spectral dimension.