{"paper":{"title":"A Quantitative Local Limit Theorem for Triangles in Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ross Berkowitz","submitted_at":"2016-10-05T06:34:02Z","abstract_excerpt":"In this paper we prove a quantiative local limit theorem for the distribution of the number of triangles in the Erd\\H{o}s-Renyi random graph $G(n,p)$, for a fixed $p\\in (0,1)$. This proof is an extension of the previous work of Gilmer and Kopparty, who proved that the local limit theorem held asymptotically for triangles. Our work gives bounds on the $\\ell^1$ and $\\ell^\\infty$ distance of the triangle distribution from a suitable discrete normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01281","kind":"arxiv","version":3},"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"}