Coupling Invasion and First Passage Percolation

Aldo Morelli

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arXiv · 2511.05618

Coupling Invasion and First Passage Percolation

Aldo Morelli

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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.

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Aldo Morelli. 2025-11-06. Coupling Invasion and First Passage Percolation. https://arxiv.org/abs/2511.05618

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