2026-07-21T15:08:02Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26279 2026-07-13T15:02:35Z ddc:004 open_access

Local Limit of Random Regular Bipartite Planar Maps Tokka, Nicolas Planar maps random maps and trees local convergence We prove the existence of the local limit of uniform random d-regular bipartite planar maps, for every d ≥ 3, as the number of vertices tends to infinity. The proof relies on a bijection between maps and so-called blossoming trees established in a previous work. After proving local convergence of the associated decorated trees, we extend the bijection to infinite trees and transfer the convergence to planar maps. The limiting object is almost surely one-ended and recurrent for the simple random walk. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nicolas Tokka 2026 Is Part Of LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2026.8 urn:nbn:de:0030-drops-262791 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.8 eng https://creativecommons.org/licenses/by/4.0/legalcode