Coupling Invasion and First Passage Percolation
arXiv:2511.05618
Abstract
It is well known that a continuous phase transition in Bernoulli bond percolation on the integer lattice is equivalent to a vanishing probability a vertex is invaded in invasion percolation. We provide a coupling between invasion percolation and first passage percolation with log-uniform passage times. This yields a new equivalent condition for a continuous phase transition in bond percolation.
10 pages, 3 figures; updated affiliation information