{"paper":{"title":"A distance exponent for Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Nina Holden, Xin Sun","submitted_at":"2016-06-03T18:30:36Z","abstract_excerpt":"Let $\\gamma \\in (0,2)$ and let $h$ be the random distribution on $\\mathbb C$ which describes a $\\gamma$-Liouville quantum gravity (LQG) cone. Also let $\\kappa = 16/\\gamma^2 >4$ and let $\\eta$ be a whole-plane space-filling SLE$_\\kappa$ curve sampled independent from $h$ and parametrized by $\\gamma$-quantum mass with respect to $h$. We study a family $\\{\\mathcal G^\\epsilon\\}_{\\epsilon>0}$ of planar maps associated with $(h, \\eta)$ called the \\textit{LQG structure graphs} (a.k.a.\\ \\textit{mated-CRT maps}) which we conjecture converge in probability in the scaling limit with respect to the Gromov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01214","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"}