{"paper":{"title":"Truncated Connectivities in a highly supercritical anisotropic percolation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bernardo N. B. de Lima, R\\'emy Sanchis, Rodrigo G. Couto","submitted_at":"2013-09-04T18:02:29Z","abstract_excerpt":"We consider an anisotropic bond percolation model on $\\mathbb{Z}^2$, with $\\textbf{p}=(p_h,p_v)\\in [0,1]^2$, $p_v>p_h$, and declare each horizontal (respectively vertical) edge of $\\mathbb{Z}^2$ to be open with probability $p_h$(respectively $p_v$), and otherwise closed, independently of all other edges. Let $x=(x_1,x_2) \\in \\mathbb{Z}^2$ with $0<x_1<x_2$, and $x'=(x_2,x_1)\\in \\mathbb{Z}^2$. It is natural to ask how the two point connectivity function $\\prob(\\{0\\leftrightarrow x\\})$ behaves, and whether anisotropy in percolation probabilities implies the strict inequality $\\prob(\\{0\\leftrighta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1120","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"}