{"paper":{"title":"Planar lattices do not recover from forest fires","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Demeter Kiss, Ioan Manolescu, Vladas Sidoravicius","submitted_at":"2013-12-25T19:07:35Z","abstract_excerpt":"Self-destructive percolation with parameters $p,\\delta$ is obtained by taking a site percolation configuration with parameter $p$, closing all sites belonging to infinite clusters, then opening every closed site with probability $\\delta$, independently of the rest. Call $\\theta(p,\\delta)$ the probability that the origin is in an infinite cluster in the configuration thus obtained. For two-dimensional lattices, we show the existence of $\\delta>0$ such that, for any $p>p_c$, $\\theta(p,\\delta)=0$. This proves the conjecture of van den Berg and Brouwer [Random Structures Algorithms 24 (2004) 480-5"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7004","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"}