{"paper":{"title":"The Number of Open Paths in Oriented Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Baptiste Gou\\'er\\'e (MAPMO), Olivier Garet, R\\'egine Marchand","submitted_at":"2013-12-09T20:35:13Z","abstract_excerpt":"We study the number $N\\_n$  of open paths of length $n$ in supercritical oriented percolation on $\\Zd \\times \\N$, with $d \\ge 1$. We prove that on the percolation event $\\{\\inf N\\_n\\textgreater{}0\\}$, $N\\_n^{1/n}$ almost surely converges to a positive deterministic constant. We also study the existence of directional limits.\nThe proof relies on the introduction of adapted sequences of regenerating times, on subadditive arguments and on the properties of the coupled zone in supercritical oriented percolation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2571","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"}