We consider standard first-passage percolation on $\mathbb{Z}^2$.
Geodesics are nearest-neighbor paths in $\mathbb{Z}^2$, each of whose segments
is time-minimizing. We prove part of the conjecture that doubly infinite
geodesics do not exist. Our main tool is a result of independent interest about
the coalescing of semi-infinite geodesics.
Publié le : 1996-01-14
Classification:
First-passage percolation,
geodesic,
disordered Ising model,
random metric,
60K35,
82B44,
60D05
@article{1042644722,
author = {Licea, Cristina and Newman, Charles M.},
title = {Geodesics in two-dimensional first-passage percolation},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 399-410},
language = {en},
url = {http://dml.mathdoc.fr/item/1042644722}
}
Licea, Cristina; Newman, Charles M. Geodesics in two-dimensional first-passage percolation. Ann. Probab., Tome 24 (1996) no. 2, pp. 399-410. http://gdmltest.u-ga.fr/item/1042644722/