{"paper":{"title":"On the critical value function in the divide and color model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andr\\'as B\\'alint, Vincent Beffara (UMPA-ENSL), Vincent Tassion (UMPA-ENSL)","submitted_at":"2011-09-15T17:14:21Z","abstract_excerpt":"The divide and color model on a graph $G$ arises by first deleting each edge of $G$ with probability $1-p$ independently of each other, then coloring the resulting connected components (\\emph{i.e.}, every vertex in the component) black or white with respective probabilities $r$ and $1-r$, independently for different components. Viewing it as a (dependent) site percolation model, one can define the critical point $r_c^G(p)$.\n  In this paper, we mainly study the continuity properties of the function $r_c^G$, which is an instance of the question of locality for percolation. Our main result is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3403","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"}