{"paper":{"title":"Finitary codings for the random-cluster model and other infinite-range monotone models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Matan Harel, Yinon Spinka","submitted_at":"2018-08-07T13:02:29Z","abstract_excerpt":"A random field $X = (X_v)_{v \\in G}$ on a quasi-transitive graph $G$ is a factor of i.i.d. if it can be written as $X=\\varphi(Y)$ for some i.i.d. process $Y= (Y_v)_{v \\in G}$ and equivariant map $\\varphi$. Such a map, also called a coding, is finitary if, for every vertex $v \\in G$, there exists a finite (but random) set $U \\subset G$ such that $X_v$ is determined by $\\{Y_u\\}_{u \\in U}$. We construct a coding for the random-cluster model on $G$, and show that the coding is finitary whenever the free and wired measures coincide. This strengthens a result of H\\\"aggstr\\\"om--Jonasson--Lyons. We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02333","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/1808.02333/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"}