{"paper":{"title":"A transition of limiting distributions of large matchings in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Cristiane M. Sato, Pu Gao","submitted_at":"2013-05-22T03:20:04Z","abstract_excerpt":"We study the asymptotic distribution of the number of matchings of size $\\ell=\\ell(n)$ in $G(n,p)$ for a wide range of $p=p(n)\\in (0,1)$ and for every $1\\le \\ell\\le \\lfloor n/2\\rfloor$. We prove that this distribution changes from normal to log-normal as $\\ell$ increases, and we determine the critical value of $\\ell$, as a function of $n$ and $p$, at which the transition of the limiting distribution occurs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5009","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"}