Boundaries of planar graphs, via circle packings

DOI10.1214/15-AOP1014zbMath1339.05061arXiv1311.3363MaRDI QIDQ726798

Omer Angel, Ori Gurel-Gurevich, Martin T. Barlow, Asaf Nachmias

Publication date: 14 July 2016

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

Full work available at URL: https://arxiv.org/abs/1311.3363

zbMATH Keywords

circle packingPoisson boundaryhyperbolicrandom walkplanar graphmartin boundary

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60) Random walks on graphs (05C81)

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Uses Software

• CirclePack

Cites Work

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• The boundary of a square tiling of a graph coincides with the Poisson boundary
• Robust discrete complex analysis: a toolbox
• Scale-invariant boundary Harnack principle in inner uniform domains
• Oded Schramm: from circle packing to SLE
• The convergence of circle packings to the Riemann mapping
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• A boundary Harnack principle in twisted Hölder domains
• Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
• Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Martin boundary of a fractal domain
• Hyperbolic and parabolic packings
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• On the equivalence of parabolic Harnack inequalities and heat kernel estimates
• Probability on Trees and Networks
• Random Walks on Infinite Graphs and Groups
• Volume growth and stochastic completeness of graphs
• BOUNDARY THEORY OF MARKOV PROCESSES (THE DISCRETE CASE)
• Minimal Positive Harmonic Functions
• Probability
• Boundary Harnack principle and Martin boundary for a uniform domain
• Harmonic functions on planar and almost planar graphs and manifolds, via circle packings