{"paper":{"title":"Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sebastian Carstens","submitted_at":"2011-03-04T13:39:49Z","abstract_excerpt":"This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists almost surely, b) at most one infinite 1*cluster exists almost surely, c) some probabilities regarding 1*clusters are bounded away from zero. Second, we show that coexistence of an infinite 1*cluster and an infinite 0cluster is almost surely impossible when the underlying probability measure is ergodic with respect to translations, positively associated, and sati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0901","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"}