{"paper":{"title":"First-order behavior of the time constant in non-isotropic continuous first-passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anne-Laure Basdevant (LPSM), Jean-Baptiste Gou\\'er\\'e (IDP), Marie Th\\'eret (FP2M, Modal'x)","submitted_at":"2024-02-12T09:30:44Z","abstract_excerpt":"Consider $\\Xi$ a homogeneous Poisson point process on $\\mathbb{R}^d$ ($d\\geq 2$) with unit intensity  with respect to the Lebesgue measure. For $\\varepsilon\\geq 0$,  we define the Boolean model $\\Sigma_{p, \\varepsilon}$ as the union of the balls of volume $\\varepsilon$ for the $p$-norm ($p\\in [1,\\infty]$) and centered at the points of $\\Xi$. We define a random pseudo-metric on $\\mathbb{R}^d$ by associating with any path a travel time equal to its $p$-length outside $\\Sigma_{p,\\varepsilon}$. This defines a continuous model of first-passage percolation, that has been studied in \\cite{GT17,GT22} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07509","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.07509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}