PreprintCC BY 4.0arXiv
Distribution tail of the distance to infinity in supercritical bond percolation
Abstract
We give an estimate for the distribution tail of the passage time between $0$ and ∞ in first-passage percolation on ℤd, 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 ∞ 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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BibTeX
@misc{verges2026distribution,
title = {{Distribution tail of the distance to infinity in supercritical bond percolation}},
author = {Julien Verges},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18033},
eprint = {2610.18033},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18033},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Distribution tail of the distance to infinity in supercritical bond percolation
AU - Julien Verges
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18033
UR - https://arxiv.org/abs/2610.18033
AB - We give an estimate for the distribution tail of the passage time between $0$ and ∞ in first-passage percolation on 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 ∞ 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 $0$.
ER -