Uniqueness and dimension for the geodesic of the critical long-range percolation metric
Probability
2025-06-13 v1
Abstract
By recent works of B\"aumler [2] and of the authors of this paper [5], the (limiting) random metric for the critical long-range percolation was constructed. In this paper, we prove the uniqueness of the geodesic between two fixed points, for which an important ingredient of independent interest is the continuity of the metric distribution. In addition, we establish the Hausdorff dimension of the geodesics.
Keywords
Cite
@article{arxiv.2506.10511,
title = {Uniqueness and dimension for the geodesic of the critical long-range percolation metric},
author = {Jian Ding and Zherui Fan and Lu-Jing Huang},
journal= {arXiv preprint arXiv:2506.10511},
year = {2025}
}
Comments
18 pages, 5 figures