{"paper":{"title":"Percolation on the stationary distributions of the voter model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Balazs Rath, Daniel Valesin","submitted_at":"2015-02-04T19:43:17Z","abstract_excerpt":"The voter model on $\\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \\geq 3$, the set of (extremal) stationary distributions is a family of measures $\\mu_\\alpha$, for $\\alpha$ between 0 and 1. A configuration sampled from $\\mu_\\alpha$ is a strongly correlated field of 0's and 1's on $\\mathbb{Z}^d$ in which the density of 1's is $\\alpha$. We consider such a configuration as a site percolation model on $\\mathbb{Z}^d$. We prove that if $d \\geq 5$, the proba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01306","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"}