{"paper":{"title":"Extreme nesting in the conformal loop ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"David B. Wilson, Jason Miller, Samuel S. Watson","submitted_at":"2013-12-31T20:57:02Z","abstract_excerpt":"The conformal loop ensemble $\\operatorname {CLE}_{\\kappa}$ with parameter $8/3<\\kappa<8$ is the canonical conformally invariant measure on countably infinite collections of noncrossing loops in a simply connected domain. Given $\\kappa$ and $\\nu$, we compute the almost-sure Hausdorff dimension of the set of points $z$ for which the number of CLE loops surrounding the disk of radius $\\varepsilon$ centered at $z$ has asymptotic growth $\\nu\\log (1/\\varepsilon )$ as $\\varepsilon \\to0$. By extending these results to a setting in which the loops are given i.i.d. weights, we give a CLE-based treatment"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0217","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"}