{"paper":{"title":"Near-critical Ornstein--Zernike theory for the planar random-cluster model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ioan Manolescu, Lucas D'Alimonte","submitted_at":"2025-10-15T15:12:21Z","abstract_excerpt":"We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with $1 \\leq q <4$ that also applies in its near-critical regime. In particular, we prove an asymptotic formula for the two-point function which holds uniformly for~$p < p_c$ and blends the subcritical and near-critical behaviours of the model.\n  The analysis is carried out by studying the renewal properties of a subcritical percolation cluster, \\emph{at the scale of the correlation length}. More precisely, we explore sequentially the cluster in a given direction, by slices of thickness comparable to the correl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.13648","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.13648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}