{"paper":{"title":"Uniqueness and universality of the Brownian map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Le Gall","submitted_at":"2011-05-24T17:34:48Z","abstract_excerpt":"We consider a random planar map $M_n$ which is uniformly distributed over the class of all rooted q-angulations with n faces. We let $\\mathbf{m}_n$ be the vertex set of $M_n$, which is equipped with the graph distance $d_\\mathrm{gr}$. Both when $q\\geq4$ is an even integer and when q=3, there exists a positive constant $c_q$ such that the rescaled metric spaces $(\\mathbf{m}_n,c_qn^{-1/4}d_\\mathrm{gr})$ converge in distribution in the Gromov-Hausdorff sense, toward a universal limit called the Brownian map. The particular case of triangulations solves a question of Schramm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4842","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"}