Uniqueness and dimension for the geodesic of the critical long-range percolation metric
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916791896244224 |
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| author | Ding, Jian Fan, Zherui Huang, Lu-Jing |
| author_facet | Ding, Jian Fan, Zherui Huang, Lu-Jing |
| contents | By recent works of Bäumler [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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness and dimension for the geodesic of the critical long-range percolation metric Ding, Jian Fan, Zherui Huang, Lu-Jing Probability 60K35, 82B27, 82B43 By recent works of Bäumler [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. |
| title | Uniqueness and dimension for the geodesic of the critical long-range percolation metric |
| topic | Probability 60K35, 82B27, 82B43 |
| url | https://arxiv.org/abs/2506.10511 |