{"paper":{"title":"SLE Loop Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dapeng Zhan","submitted_at":"2017-02-26T12:40:59Z","abstract_excerpt":"We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE$_\\kappa$ loop measures for $\\kappa\\in(0,8)$. First, we construct rooted SLE$_\\kappa$ loop measures in the Riemann sphere $\\widehat{\\mathbb C}$, which satisfy M\\\"obius covariance, conformal Markov property, reversibility, and space-time homogeneity, when the loop is parametrized by its $(1+\\frac \\kappa 8)$-dimensional Minkowski content. Second, by integrating rooted SLE$_\\kappa$ loop measures, we construct the unrooted SLE$_\\kappa$ loop measure in $\\widehat{\\mathbb C}$, which satisfies M\\\"obius inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08026","kind":"arxiv","version":4},"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"}