Planarity and non-separating cycles in uniform high genus quadrangulations-Reference-Cited by-同舟云学术

Planarity and non-separating cycles in uniform high genus quadrangulations

Published:2021-04-05 Issue: Volume: Page:
ISSN:0178-8051
Container-title:Probability Theory and Related Fields
language:en
Short-container-title:Probab. Theory Relat. Fields

Author:

Louf Baptiste^ORCID

Abstract

AbstractWe study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.

Funder

Knut och Alice Wallenbergs Stiftelse

Publisher

Springer Science and Business Media LLC

Subject

Statistics, Probability and Uncertainty,Statistics and Probability,Analysis

Link

http://link.springer.com/content/pdf/10.1007/s00440-021-01050-8.pdf

Reference29 articles.

1. Angel, O., Chapuy, G., Curien, N., Ray, G.: The local limit of unicellular maps in high genus. Electron. Commun. Probab. 18(86), 1–8 (2013)

2. Angel, O., Schramm, O.: Uniform infinite planar triangulations. Comm. Math. Phys. 241(2–3), 191–213 (2003)

3. Bender, E.A., Canfield, E.: The asymptotic number of rooted maps on a surface. J. Combinat. Theory Ser. A 43(2), 244–257 (1986)

4. Bettinelli, J.: Geodesics in Brownian surfaces (Brownian maps). Ann. Inst. Henri Poincaré Probab. Stat. 52(2), 612–646 (2016)

5. Bodini, O., Courtiel, J., Dovgal, S., Hwang, H.-K.: Asymptotic distribution of parameters in random maps. In: 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, volume 110 of LIPIcs. Leibniz Int. Proc. Inform., pages Art. No. 13, 12. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, (2018)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Random graphs embeddable in order‐dependent surfaces;Random Structures & Algorithms;2023-12-05

2. Unicellular maps vs. hyperbolic surfaces in large genus: Simple closed curves;The Annals of Probability;2023-05-01

3. Short cycles in high genus unicellular maps;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2022-08-01