{"paper":{"title":"On the probability of nonexistence in binomial subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Andreas Noever, Frank Mousset, Konstantinos Panagiotou, Wojciech Samotij","submitted_at":"2017-11-16T17:48:38Z","abstract_excerpt":"Given a hypergraph $\\Gamma=(\\Omega,\\mathcal{X})$ and a sequence $\\mathbf{p} = (p_\\omega)_{\\omega\\in \\Omega}$ of values in $(0,1)$, let $\\Omega_{\\mathbf{p}}$ be the random subset of $\\Omega$ obtained by keeping every vertex $\\omega$ independently with probability $p_\\omega$. We investigate the general question of deriving fine (asymptotic) estimates for the probability that $\\Omega_{\\mathbf{p}}$ is an independent set in $\\Gamma$, which is an omnipresent problem in probabilistic combinatorics. Our main result provides a sequence of upper and lower bounds on this probability, each of which can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06216","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"}