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- W3103751552 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." @default.
- W3103751552 created "2020-11-23" @default.
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- W3103751552 date "2017-01-01" @default.
- W3103751552 modified "2023-09-25" @default.
- W3103751552 title "Boundaries of planar graphs: a unified approach" @default.
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- W3103751552 doi "https://doi.org/10.1214/17-ejp116" @default.
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