{"paper":{"title":"Critical exponents on Fortuin--Kasteleyn weighted planar maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Beno\\^it Laslier, Gourab Ray, Nathana\\\"el Berestycki","submitted_at":"2015-02-02T12:24:47Z","abstract_excerpt":"In this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \\in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain rigorously the value of the critical exponent associated with the length of cluster interfaces, which is shown to be $$\n  \\frac{4}{\\pi} \\arccos \\left( \\frac{\\sqrt{2 - \\sqrt{q}}}{2} \\right)=\\frac{\\kappa'}{8}. $$ where $\\kappa' $ is the SLE parameter associated with this model. We also derive the exponent corresponding to the area enclosed by a loop which is shown to be 1 for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00450","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"}