Geodesics in first-passage percolation cross any pattern
Probability
2023-03-09 v3
Abstract
In first-passage percolation, one places nonnegative i.i.d. random variables (T (e)) on the edges of Z d. A geodesic is an optimal path for the passage times T (e). Consider a local property of the time environment. We call it a pattern. We investigate the number of times a geodesic crosses a translate of this pattern. Under mild conditions, we show that, apart from an event with exponentially small probability, this number is linear in the distance between the extremities of the geodesic.
Cite
@article{arxiv.2204.02021,
title = {Geodesics in first-passage percolation cross any pattern},
author = {Antonin Jacquet},
journal= {arXiv preprint arXiv:2204.02021},
year = {2023}
}
Comments
Minor changes in the introduction