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.
Publié le : 1996-07-14
Classification:
Planar graphs,
random walks,
harmonic measure,
Dirichlet problem,
60J15,
60J45,
52C20
@article{1065725179,
author = {Benjamini, Itai and Schramm, Oded},
title = {Random walks and harmonic functions on infinite planar graphs
using square tilings},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1219-1238},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725179}
}
Benjamini, Itai; Schramm, Oded. Random walks and harmonic functions on infinite planar graphs
using square tilings. Ann. Probab., Tome 24 (1996) no. 2, pp. 1219-1238. http://gdmltest.u-ga.fr/item/1065725179/