Separating cycles and isoperimetric inequalities in the uniform infinite planar quadrangulation

DOI10.1214/18-AOP1289zbMath1414.05267arXiv1710.02990OpenAlexW2962756441WikidataQ127928589 ScholiaQ127928589MaRDI QIDQ2421821

Thomas Lehéricy, Jean-François Le Gall

Publication date: 18 June 2019

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02990

zbMATH Keywords

isoperimetric inequalityuniform infinite planar quadrangulationskeleton decompositionseparating cycletruncated hull

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random graphs (graph-theoretic aspects) (05C80)

Related Items (7)

First-passage percolation in random planar maps and Tutte's bijection ⋮ How fast planar maps get swallowed by a peeling process ⋮ Brownian geometry ⋮ Convergence of Eulerian triangulations ⋮ The skeleton of the UIPT, seen from infinity ⋮ Recurrence of the uniform infinite half-plane map via duality of resistances ⋮ Isoperimetric inequalities in the Brownian plane

Cites Work

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• Local limit of labeled trees and expected volume growth in a random quadrangulation
• A view from infinity of the uniform infinite planar quadrangulation
• Uniform infinite planar quadrangulations with a boundary
• Volumes in the Uniform Infinite Planar Triangulation: From Skeletons to Generating Functions
• Scaling limits of random trees and planar maps

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