A critical exponent for shortest-path scaling in continuum percolation

Abstract

We carry out Monte Carlo experiments to study the scaling behavior of shortest path lengths in continuum percolation. These studies suggest that the critical exponent governing this scaling is the same for both continuum and lattice percolation. We use splitting, a technique that has not yet been fully exploited in the physics literature, to increase the speed of our simulations. This technique can also be applied to other models where clusters are grown sequentially.