Year: 2026
Type: preprint
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 $0$.
Source: arXiv (Cornell University)
Author: Verges, Julien
Institution: Stockholm University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221798659