{"paper":{"title":"Competitive Erosion is Conformally Invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CV"],"primary_cat":"math.PR","authors_text":"Shirshendu Ganguly, Yuval Peres","submitted_at":"2015-03-24T11:21:52Z","abstract_excerpt":"We study a graph-theoretic model of interface dynamics called $Competitive\\, Erosion$. Each vertex of the graph is occupied by a particle, which can be either red or blue. New red and blue particles are emitted alternately from their respective bases and perform random walk. On encountering a particle of the opposite color they remove it and occupy its position. We consider competitive erosion on discretizations of `smooth', planar, simply connected domains. The main result of this article shows that at stationarity, with high probability, the blue and the red regions are separated by the leve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06989","kind":"arxiv","version":4},"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"}