{"paper":{"title":"The Order of the Giant Component of Random Hypergraphs","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Amin Coja-Oghlan, Michael Behrisch, Mihyun Kang","submitted_at":"2007-06-04T18:40:46Z","abstract_excerpt":"We establish central and local limit theorems for the number of vertices in the largest component of a random $d$-uniform hypergraph $\\hnp$ with edge probability $p=c/\\binnd$, where $(d-1)^{-1}+\\eps<c<\\infty$. The proof relies on a new, purely probabilistic approach, and is based on Stein's method as well as exposing the edges of $H_d(n,p)$ in several rounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0496","kind":"arxiv","version":1},"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"}