Brochette first-passage percolation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915936791953408 |
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| author | Marivain, Maxime |
| author_facet | Marivain, Maxime |
| contents | We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point convergence theorem, identifying the time constant. In particular, we explore the case where the time constant vanishes and demonstrate the existence of a wide range of possible behaviours. Next, we prove a shape theorem, showing that the limiting shape is the $L^1$ diamond. Finally, we extend the analysis by proving a point-to-point convergence theorem in the setting where passage times are allowed to be infinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brochette first-passage percolation Marivain, Maxime Probability We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point convergence theorem, identifying the time constant. In particular, we explore the case where the time constant vanishes and demonstrate the existence of a wide range of possible behaviours. Next, we prove a shape theorem, showing that the limiting shape is the $L^1$ diamond. Finally, we extend the analysis by proving a point-to-point convergence theorem in the setting where passage times are allowed to be infinite. |
| title | Brochette first-passage percolation |
| topic | Probability |
| url | https://arxiv.org/abs/2501.11398 |