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arXiv · 2603.03257

Supercritical sharpness of percolation

Sahar Diskin·Philip Easo·Ritvik Ramanan Radhakrishnan·Benny Sudakov·Vincent Tassion
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Abstract

We prove that for supercritical percolation on every infinite transitive graph, the probability that the origin belongs to a finite cluster of size at least $n$ decays exponentially in $\Phi(n)$, where $\Phi$ is the isoperimetric function of the graph.

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Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan, Benny Sudakov, Vincent Tassion. 2026-03-03. Supercritical sharpness of percolation. https://arxiv.org/abs/2603.03257

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