{"paper":{"title":"Factorization Formulas for $2D$ Critical Percolation, Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rene Conijn","submitted_at":"2015-02-15T23:32:58Z","abstract_excerpt":"We consider critical site percolation on the triangular lattice in the upper half-plane. Let $u_1, u_2$ be two sites on the boundary and $w$ a site in the interior of the half-plane. It was predicted by Simmons, Kleban and Ziff in a paper from 2007 that the ratio $\\mathbb{P}(nu_1 \\leftrightarrow nu_2 \\leftrightarrow nw)^{2}\\,/\\,\\mathbb{P}(nu_1 \\leftrightarrow nu_2)\\cdot\\mathbb{P}(nu_1 \\leftrightarrow nw)\\cdot\\mathbb{P}(nu_2 \\leftrightarrow nw)$ converges to $K_F$ as $n \\to \\infty$, where $x\\leftrightarrow y$ denotes the event that $x$ and $y$ are in the same open cluster, and $K_F$ is an expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04387","kind":"arxiv","version":3},"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"}