Geodesics and Wandering Exponents in Brochette First-Passage Percolation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914592508084224 |
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| author | Marivain, Maxime |
| author_facet | Marivain, Maxime |
| contents | We study geodesics in the Brochette first-passage percolation model, where edges on the same axis-parallel line share a common random passage time, inducing long-range dependence. We focus on the maximal transversal deviation H n of geodesics from the origin to ne 1 . We prove existence of geodesics under mild assumptions and establish the order of magnitude of H n depending on the behavior of the passage-time distribution near its infimum. These results yield explicit wandering exponents in this dependent setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23718 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geodesics and Wandering Exponents in Brochette First-Passage Percolation Marivain, Maxime Probability We study geodesics in the Brochette first-passage percolation model, where edges on the same axis-parallel line share a common random passage time, inducing long-range dependence. We focus on the maximal transversal deviation H n of geodesics from the origin to ne 1 . We prove existence of geodesics under mild assumptions and establish the order of magnitude of H n depending on the behavior of the passage-time distribution near its infimum. These results yield explicit wandering exponents in this dependent setting. |
| title | Geodesics and Wandering Exponents in Brochette First-Passage Percolation |
| topic | Probability |
| url | https://arxiv.org/abs/2605.23718 |