DROPS

Document

DOI: 10.4230/LIPIcs.AofA.2026.8

Local Limit of Random Regular Bipartite Planar Maps

Authors: Nicolas Tokka

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)

Abstract

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.

Cite as

Nicolas Tokka. Local Limit of Random Regular Bipartite Planar Maps. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{tokka:LIPIcs.AofA.2026.8,
  author =	{Tokka, Nicolas},
  title =	{{Local Limit of Random Regular Bipartite Planar Maps}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.8},
  URN =		{urn:nbn:de:0030-drops-262791},
  doi =		{10.4230/LIPIcs.AofA.2026.8},
  annote =	{Keywords: Planar maps, random maps and trees, local convergence}
}

Search Results

Documents authored by Tokka, Nicolas

Local Limit of Random Regular Bipartite Planar Maps

Abstract

Cite as

Thanks for your feedback!

Could not send message