{"paper":{"title":"On replica symmetry of large deviations in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Eyal Lubetzky, Yufei Zhao","submitted_at":"2012-10-25T22:27:32Z","abstract_excerpt":"The following question is due to Chatterjee and Varadhan (2011). Fix $0<p<r<1$ and take $G\\sim G(n,p)$, the Erd\\H{o}s-R\\'enyi random graph with edge density $p$, conditioned to have at least as many triangles as the typical $G(n,r)$. Is $G$ close in cut-distance to a typical $G(n,r)$? Via a beautiful new framework for large deviation principles in $G(n,p)$, Chatterjee and Varadhan gave bounds on the replica symmetric phase, the region of $(p,r)$ where the answer is positive. They further showed that for any small enough $p$ there are at least two phase transitions as $r$ varies.\n  We settle th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7013","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"}