{"paper":{"title":"Connectivity of the adjacency graph of complementary components of the SLE fan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cillian Doherty, Jason Miller, Konstantinos Kavvadias","submitted_at":"2024-11-20T08:56:54Z","abstract_excerpt":"Suppose that $h$ is an instance of the Gaussian free field (GFF) on a simply connected domain $D \\subseteq {\\mathbf C}$ and $x,y \\in \\partial D$ are distinct. Fix $\\kappa \\in (0,4)$ and for each $\\theta \\in {\\mathbf R}$ let $\\eta_\\theta$ be the flow line of $h$ from $x$ to $y$. Recall that for $\\theta_1 < \\theta_2$ the fan ${\\mathbf F}(\\theta_1,\\theta_2)$ of flow lines of $h$ from $x$ to $y$ is the closure of the union of $\\eta_\\theta$ as $\\theta$ varies in any fixed countable dense subset of $[\\theta_1,\\theta_2]$. We show that the adjacency graph of components of $D \\setminus {\\mathbf F}(\\the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13133","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/2411.13133/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"}