{"paper":{"title":"Maximal stream and minimal cutset for first passage percolation through a domain of $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marie Th\\'eret, Rapha\\\"el Cerf","submitted_at":"2012-01-24T08:01:17Z","abstract_excerpt":"We consider the standard first passage percolation model in the rescaled graph $\\mathbb{Z}^d/n$ for $d\\geq2$ and a domain $\\Omega$ of boundary $\\Gamma$ in $\\mathbb{R}^d$. Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$, representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. A law of large numbers for the maximal flow from $\\Gamma ^1$ to $\\Gamma ^2$ in $\\Omega$ is already known. In this paper we investigate the asymptotic behavior of a maximal stream and a minimal cutset. A maximal stream is a vector measure $\\vec{\\mu}_n^{\\max}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4921","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"}