{"paper":{"title":"The time constant and critical probabilities in percolation models","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Leandro P.R. Pimentel","submitted_at":"2004-11-24T17:58:00Z","abstract_excerpt":"We consider a first-passage percolation model on a Delaunay triangulation of the plane. In this model each edge is independently equipped with a nonnegative random variable, with distribution function F, which is interpreted as the time it takes to traverse the edge. Vahidi-Asl and Wierman have shown that, under a suitable moment condition on F, the minimum time taken to reach a point x from the origin 0 is asymptotically \\mu(F)|x|, where \\mu(F) is a nonnegative finite constant. However the exact value of the time constant \\mu(F) still a fundamental problem in percolation theory. Here we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411560","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}