Diffusion in random structures with a topological bias

We study biased diffusion on a topological random comb with an exponential distribution of dangling ends which is relevant to the essential physics of biased diffusion in random structures such as percolation systems above criticality. By mapping the problem onto a linear chain with a power-law distribution of transition rates we find that above a bias threshold, diffusion is anomalous in two respects: $d_w$ (the fractal dimension of a random walk) is above 1, and depends continuously upon the magnitude of the bias. Our analytic results are confirmed by extensive computer simulations.