Optimal Path in Strong Disorder and Shortest Path in Invasion Percolation with Trapping

Abstract

We present analytical and numerical results suggesting that the optimal path in an energy landscape in the strong disorder limit is in the universality class of the shortest path in invasion percolation with trapping. Our results imply that, in contrast to common belief, invasion percolation with trapping and regular percolation in $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ are in different universality classes.