{"paper":{"title":"Bipolar orientations on planar maps and SLE$_{12}$","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, Richard Kenyon, Scott Sheffield","submitted_at":"2015-11-12T20:52:36Z","abstract_excerpt":"We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the \"peano curve\" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a $\\sqrt{4/3}$-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter $\\kappa=12$ (i.e., SLE$_{12}$). This result is universal in the sense that it holds for bipolar-oriented triangulations, quadrangulations, $k$-angulati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04068","kind":"arxiv","version":2},"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"}