Supercritical sharpness of percolation
Probability
2026-03-04 v1
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 decays exponentially in , where is the isoperimetric function of the graph.
Keywords
Cite
@article{arxiv.2603.03257,
title = {Supercritical sharpness of percolation},
author = {Sahar Diskin and Philip Easo and Ritvik Ramanan Radhakrishnan and Benny Sudakov and Vincent Tassion},
journal= {arXiv preprint arXiv:2603.03257},
year = {2026}
}