Scaling law for the contact-propagation regime of first-passage percolation

Abstract

We study first-passage percolation on a lattice with a fraction p≲$p_c$ of bonds assigned zero time delay, the others having finite delays governed by the cumulative distribution F(x). This ‘‘contact-propagation’’ regime exhibits criticality analogous to the random superconducting network. We derive, and confirm numerically, a scaling law that relates the divergence of the first-passage velocity near the percolation threshold $p_c$ to static percolation exponents and to F(x).