{"paper":{"title":"Upper large deviations for the maximal flow through a domain of $\\bolds{\\mathbb{R}^d}$ in first passage percolation","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":"2009-07-31T10:44:54Z","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 $\\Omega$. We investigate the asymptotic behavior of the flow $\\phi_n$ through a discrete version $\\Omega_n$ of $\\Omega$ between the corresponding discrete sets $\\Gamma ^1_n$ and $\\Gamma ^2_n$. We prove that under some conditions on the regularity of the domain and on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5499","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"}