{"paper":{"title":"Continuity of the time constant in a continuous model of first passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Baptiste Gou\\'er\\'e (IDP), Marie Th\\'eret (FP2M, Modal'x)","submitted_at":"2020-11-27T07:52:56Z","abstract_excerpt":"For a given dimension d $\\ge$ 2 and a finite measure $\\nu$ on (0, +$\\infty$), we consider $\\xi$ a Poisson point process on R d x (0, +$\\infty$) with intensity measure dc $\\otimes$ $\\nu$ where dc denotes the Lebesgue measure on R d. We consider the Boolean model $\\Sigma$ = $\\cup$ (c,r)$\\in$$\\xi$ B(c, r) where B(c, r) denotes the open ball centered at c with radius r. For every x, y $\\in$ R d we define T (x, y) as the minimum time needed to travel from x to y by a traveler that walks at speed 1 outside $\\Sigma$ and at infinite speed inside $\\Sigma$. By a standard application of Kingman sub-addit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13595","kind":"arxiv","version":1},"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/2011.13595/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"}