{"paper":{"title":"Tightness of approximations to metrics on non-simple conformal loop ensemble gaskets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jason Miller, Valeria Ambrosio, Yizheng Yuan","submitted_at":"2025-07-21T13:11:54Z","abstract_excerpt":"We study a class of approximation schemes aimed at constructing conformally covariant metrics defined in the gasket of a conformal loop ensemble (CLE$_\\kappa$) for $\\kappa \\in (4,8)$. This is the range of parameter values so that the loops of a CLE$_\\kappa$ intersect themselves, each other, and the domain boundary. Its gasket is the closure of the union of the set of points not surrounded by a loop. The class of approximation schemes includes approximations to the geodesic metric and to the resistance metric. We show that the laws of these approximations are tight, and that every subsequential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15589","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.15589/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"}