Key points are not available for this paper at this time.
Simple conditions are presented under which the fractal dimension of a random walk on an aggregate, dₖ, is given by dₖ=D+1, where D is the aggregate's fractal dimension. These conditions are argued (with one simple speculative assumption) to apply for D<2, implying a breakdown of the Alexander-Orbach rule dₖ=3D2. Existing results for percolation clusters, lattice animals, and diffusion-limited aggregates seem to favor our new rule.
Aharony et al. (Mon,) studied this question.