{"paper":{"title":"The Williams Bjerknes Model on Regular Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexander Vandenberg-Rodes, Oren Louidor, Ran J. Tessler","submitted_at":"2012-11-24T18:56:39Z","abstract_excerpt":"We consider the Williams Bjerknes model, also known as the biased voter model on the $d$-regular tree $\\bbT^d$, where $d \\geq 3$. Starting from an initial configuration of \"healthy\" and \"infected\" vertices, infected vertices infect their neighbors at Poisson rate $\\lambda \\geq 1$, while healthy vertices heal their neighbors at Poisson rate 1. All vertices act independently. It is well known that starting from a configuration with a positive but finite number of infected vertices, infected vertices will continue to exist at all time with positive probability iff $\\lambda > 1$. We show that ther"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5694","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"}