OPTIMAL PATH IN STRONG DISORDER AND SHORTEST PATH IN INVASION PERCOLATION WITH TRAPPING

with dopt 1.22 6 0.01 in d 2, dopt 1.42 6 0.02 in d 3, and dopt 1.59 6 0.02 in d 4 [6,7], which is different from the scaling of the shortest path in regular percolation [8]. Moreover, they introduced a new variant of invasion percolation (compressible invasion percolation, see below, where loops are forbidden to occur), and showed that the shortest path in this model is in the same universality class as the optimal path in the strong disorder limit [7].