{"paper":{"title":"A mating-of-trees approach for graph distances in random planar maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Nina Holden, Xin Sun","submitted_at":"2017-11-02T13:22:09Z","abstract_excerpt":"We introduce a general technique for proving estimates for certain random planar maps which belong to the $\\gamma$-Liouville quantum gravity (LQG) universality class for $\\gamma \\in (0,2)$. The family of random planar maps we consider are those which can be encoded by a two-dimensional random walk with i.i.d.\\ increments via a mating-of-trees bijection, and includes the uniform infinite planar triangulation (UIPT; $\\gamma=\\sqrt{8/3}$); and planar maps weighted by the number of different spanning trees ($\\gamma=\\sqrt 2$), bipolar orientations ($\\gamma=\\sqrt{4/3}$), or Schnyder woods ($\\gamma=1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00723","kind":"arxiv","version":3},"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/1711.00723/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"}