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Local Limit of Random Regular Bipartite Planar Maps

Author Nicolas Tokka

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LIPIcs.AofA.2026.8.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Generating functions
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Random graphs
  • Mathematics of computing → Probability and statistics
Keywords
  • Planar maps
  • random maps and trees
  • local convergence

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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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.AofA.2026.8

Author Details

Nicolas Tokka
  • MODAL'X, Université Paris-Nanterre, France
  • IRIF, Université Paris-Cité, France

Funding

ANR IsOMa "ANR-21-CE48-0007"

Acknowledgements

We sincerely thank Marie Albenque and Laurent Ménard for their thoughtful review and valuable advice throughout this work.

References

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