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July 1996 Random walks and harmonic functions on infinite planar graphs using square tilings
Itai Benjamini, Oded Schramm
Ann. Probab. 24(3): 1219-1238 (July 1996). DOI: 10.1214/aop/1065725179

Abstract

We study a wide class of transient planar graphs, through a geometric model given by a square tiling of a cylinder. For many graphs, the geometric boundary of the tiling is a circle and is easy to describe in general. The simple random walk on the graph converges (with probability 1) to a point in the geometric boundary. We obtain information on the harmonic measure and estimates on the rate of convergence. This allows us to extend results we previously proved for triangulations of a disk.

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Itai Benjamini. Oded Schramm. "Random walks and harmonic functions on infinite planar graphs using square tilings." Ann. Probab. 24 (3) 1219 - 1238, July 1996. https://doi.org/10.1214/aop/1065725179

Information

Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0862.60053
MathSciNet: MR1411492
Digital Object Identifier: 10.1214/aop/1065725179

Subjects:
Primary: 52C20, 60J15, 60J45

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 3 • July 1996
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