Nonuniversality of diffusion exponents in percolation systems

We study diffusion on the incipient infinite percolation cluster in d=2 with a power-law distribution of transition rates P(W)W-±, ±<1. Using the exact enumeration method we find that the diffusion exponent d»w(±) sticks at its ±=-z value for ±0. For ±>0, d»w is bounded by df+1[(1-±)]d»w(±) d»w(-z)+±[(1-±)]. Specifically, for small ± our numerical results are close to the upper bound, while for larger ± they are close to the lower bound.