{"paper":{"title":"Upper tails for triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Bobby DeMarco, Jeff Kahn","submitted_at":"2010-05-25T02:54:24Z","abstract_excerpt":"With $\\xi$ the number of triangles in the usual (Erd\\H{o}s-R\\'enyi) random graph $G(m,p)$, $p>1/m$ and $\\eta>0$, we show (for some $C_{\\eta}>0$) $$\\Pr(\\xi> (1+\\eta)\\E \\xi) < \\exp[-C_{\\eta}\\min{m^2p^2\\log(1/p),m^3p^3}].$$ This is tight up to the value of $C_{\\eta}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4471","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"}