{"paper":{"title":"A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Jonathan A. Noel, Natasha Morrison","submitted_at":"2018-06-07T21:01:54Z","abstract_excerpt":"Given a hypergraph $\\mathcal{H}$, the $\\mathcal{H}$-bootstrap process starts with an initial set of infected vertices of $\\mathcal{H}$ and, at each step, a healthy vertex $v$ becomes infected if there exists a hyperedge of $\\mathcal{H}$ in which $v$ is the unique healthy vertex. We say that the set of initially infected vertices percolates if every vertex of $\\mathcal{H}$ is eventually infected. We show that this process exhibits a sharp threshold when $\\mathcal{H}$ is a hypergraph obtained by randomly sampling hyperedges from an approximately $d$-regular $r$-uniform hypergraph satisfying some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02903","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.02903/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}