{"paper":{"title":"Confidence intervals for the critical value 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":"2013-07-10T11:21:06Z","abstract_excerpt":"We obtain confidence intervals for the location of the percolation phase transition in H\\\"aggstr\\\"om's divide and color model on the square lattice $\\mathbb{Z}^2$ and the hexagonal lattice $\\mathbb{H}$. The resulting probabilistic bounds are much tighter than the best deterministic bounds up to date; they give a clear picture of the behavior of the DaC models on $\\mathbb{Z}^2$ and $\\mathbb{H}$ and enable a comparison with the triangular lattice $\\mathbb{T}$. In particular, our numerical results suggest similarities between DaC model on these three lattices that are in line with universality co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2755","kind":"arxiv","version":1},"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"}