Abstract
Simple conditions are presented under which the fractal dimension of a random walk on an aggregate, , is given by , where is the aggregate's fractal dimension. These conditions are argued (with one simple speculative assumption) to apply for , implying a breakdown of the Alexander-Orbach rule . Existing results for percolation clusters, lattice animals, and diffusion-limited aggregates seem to favor our new rule.
- Received 26 January 1984
DOI:https://doi.org/10.1103/PhysRevLett.52.2368
©1984 American Physical Society