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arXiv · 2610.18033

Distribution tail of the distance to infinity in supercritical bond percolation

Julien Verges
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Abstract

We give an estimate for the distribution tail of the passage time between $0$ and $\infty$ in first-passage percolation on $\mathbb Z^d$, when the weight distribution is bounded and has a supercritical atom at $0$. A special case involves the number of disjoint cutsets between $0$ and $\infty$ in supercritical bond percolation. Besides, we show that the rate function for the upper-tail deviations of the point-to-point passage time is asymptotically polynomial near $0$.

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Julien Verges. 2026-10-13. Distribution tail of the distance to infinity in supercritical bond percolation. https://arxiv.org/abs/2610.18033

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