{"paper":{"title":"Upper large deviations for the maximal flow in first passage percolation","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marie Th\\'eret","submitted_at":"2006-07-11T11:10:23Z","abstract_excerpt":"We consider the standard first passage percolation in $\\mathbb{Z}^{d}$ for $d\\geq 2$ and we denote by $\\phi_{n^{d-1},h(n)}$ the maximal flow through the cylinder $]0,n]^{d-1} \\times ]0,h(n)]$ from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension three: under some assumptions, $\\phi_{n^{d-1},h(n)} / n^{d-1}$ converges towards a constant $\\nu$. We look now at the probability that $\\phi_{n^{d-1},h(n)} / n^{d-1}$ is greater than $\\nu + \\epsilon$ for some $\\epsilon >0$, and we show under some assumptions that this probability decays exponentially fast wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607253","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"}