Diffusion with a topological bias on random structures with a power-law distribution of dangling ends

We study diffusion with a topological bias on random structures having dangling ends whose length L is chosen from a power-law distribution P(L)∼L-(α+1). We find that the mean-square displacement x2 of a random walker on the backbone varies asymptotically as x2∼(logt)2α, slower than any power of t, in contrast with x∼t, the conventional result for a nonrandom lattice. Our predictions are confirmed by numerical simulations for percolation and for the random comb.