{"paper":{"title":"Asymptotics for $2D$ Critical First Passage Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael Damron, Wai-Kit Lam, Xuan Wang","submitted_at":"2015-05-28T04:18:07Z","abstract_excerpt":"We consider first-passage percolation on $\\mathbb{Z}^2$ with i.i.d. weights, whose distribution function satisfies $F(0) = p_c = 1/2$. This is sometimes known as the \"critical case\" because large clusters of zero-weight edges force passage times to grow at most logarithmically, giving zero time constant. Denote $T(\\mathbf{0}, \\partial B(n))$ as the passage time from the origin to the boundary of the box $[-n,n] \\times [-n,n]$. We characterize the limit behavior of $T(\\mathbf{0}, \\partial B(n))$ by conditions on the distribution function $F$. We also give exact conditions under which $T(\\mathbf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07544","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"}