{"paper":{"title":"A discontinuous phase transition in the threshold-$\\theta \\geq 2$ contact process on random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Danny Nam","submitted_at":"2019-07-11T05:41:10Z","abstract_excerpt":"We study the discrete-time threshold-$\\theta \\geq 2$ contact process on random graphs of general degrees. For random graphs with a given degree distribution $\\mu$, we show that if $\\mu$ is lower bounded by $\\theta+2$ and has finite $k$th moments for all $k>0$, then the discrete-time threshold-$\\theta$ contact process on the random graph exhibits a discontinuous phase transition in the emergence of metastability, thus answering a question of Chatterjee and Durrett \\cite{cd13}. To be specific, we establish that (i) for any large enough infection probability $p>p_1$, the process started from the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05005","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"}