{"paper":{"title":"The contact process on finite homogeneous trees revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Valesin, Jean-Christophe Mourrat, Michael Cranston, Thomas Mountford","submitted_at":"2014-03-24T12:09:00Z","abstract_excerpt":"We consider the contact process with infection rate $\\lambda$ on $\\mathbb{T}_n^d$, the $d$-ary tree of height $n$. We study the extinction time $\\tau_{\\mathbb{T}_n^d}$, that is, the random time it takes for the infection to disappear when the process is started from full occupancy. We prove two conjectures of Stacey regarding $\\tau_{\\mathbb{T}_n^d}$. Let $\\lambda_2$ denote the upper critical value for the contact process on the infinite $d$-ary tree. First, if $\\lambda < \\lambda_2$, then $\\tau_{\\mathbb{T}_n^d}$ divided by the height of the tree converges in probability, as $n \\to \\infty$, to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5927","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"}