{"paper":{"title":"First passage percolation and escape strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enrique D. Andjel, Maria Eulalia Vares","submitted_at":"2012-07-14T20:01:54Z","abstract_excerpt":"Consider first passage percolation on $\\mathbb{Z}^d$ with passage times given by i.i.d. random variables with common distribution $F$. Let $t_\\pi(u,v)$ be the time from $u$ to $v$ for a path $\\pi$ and $t(u,v)$ the minimal time among all paths from $u$ to $v$. We ask whether or not there exist points $x,y \\in \\mathbb{Z}^d$ and a semi-infinite path $\\pi=(y_0=y,y_1,\\dots)$ such that $t_\\pi(y, y_{n+1})<t(x,y_n)$ for all $n$. Necessary and sufficient conditions on $F$ are given for this to occur. When the support of $F$ is unbounded, we also obtain results on the number of edges with large passage "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3456","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":""},"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"}