Translator Disclaimer
2017 Boundaries of planar graphs: a unified approach
Tom Hutchcroft, Yuval Peres
Electron. J. Probab. 22: 1-20 (2017). DOI: 10.1214/17-EJP116

Abstract

We give a new proof that the Poisson boundary of a planar graph coincides with the boundary of its square tiling and with the boundary of its circle packing, originally proven by Georgakopoulos [9] and Angel, Barlow, Gurel-Gurevich and Nachmias [2] respectively. Our proof is robust, and also allows us to identify the Poisson boundaries of graphs that are rough-isometric to planar graphs.

We also prove that the boundary of the square tiling of a bounded degree plane triangulation coincides with its Martin boundary. This is done by comparing the square tiling of the triangulation with its circle packing.

Citation

Download Citation

Tom Hutchcroft. Yuval Peres. "Boundaries of planar graphs: a unified approach." Electron. J. Probab. 22 1 - 20, 2017. https://doi.org/10.1214/17-EJP116

Information

Received: 13 August 2016; Accepted: 9 October 2017; Published: 2017
First available in Project Euclid: 25 November 2017

zbMATH: 1378.05189
MathSciNet: MR3733658
Digital Object Identifier: 10.1214/17-EJP116

Subjects:
Primary: 05C81

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.22 • 2017
Back to Top