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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0607253","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-07-11T11:10:23Z","cross_cats_sorted":[],"title_canon_sha256":"02ac1e1a24c487e6399894c89076a3287283566fb218636708b5e318a232bd5c","abstract_canon_sha256":"aad530ac307ad6a8596f8c16b29c881c204277a90cc16025fa253f33a813d7bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:53.376992Z","signature_b64":"BBlolypJKxunmlRz1k+8VE7HZ267v5WG2aAZN8exLH1bf5WPpxQCn1FfyJPxm/qypAkChqBBjs5TYSj08eq7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d16db4ff94532242cec60b7c12cec7d4a0405a3ddb4bc17457490d5ffc603cd8","last_reissued_at":"2026-05-18T04:08:53.376337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:53.376337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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