{"paper":{"title":"The Contact Process on Periodic Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Brandon Zhao, Grayson York, Matthew Junge, Remy Kassem, Rick Durrett, Xiangying Huang, Yufeng Jiang","submitted_at":"2018-08-06T13:02:26Z","abstract_excerpt":"A little over 25 years ago Pemantle pioneered the study of the contact process on trees, and showed that the critical values $\\lambda_1$ and $\\lambda_2$ for global and local survival were different. Here, we will consider the case of trees in which the degrees of vertices are periodic. We will compute bounds on $\\lambda_1$ and $\\lambda_2$ and for the corresponding critical values $\\lambda_g$ and $\\lambda_\\ell$ for branching random walk. Much of what we find for period two $(a,b)$ trees was known to Pemantle. However, two significant new results give sharp asymptotics for the critical value $\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01863","kind":"arxiv","version":3},"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"}