An H-geodesic is a doubly infinite path which locally
minimizes the passage time in the i.i.d. first passage percolation model on a
half-plane H. Under the assumption that the bond passage times are
continuously distributed with a finite mean, we prove that, with probability 1,
H-geodesics do not exist. As a corollary we show that, with probability
1, any geodesic in the analogous model on the whole plane $\mathbf{Z}^2$ has to
intersect all straight lines with rational slopes.
Publié le : 1998-01-14
Classification:
First-passage percolation,
time-minimizing paths,
infinite geodesics,
ergodicity,
large deviation bounds,
60K35,
82B44,
82D30
@article{1022855423,
author = {Wehr, Jan and Woo, Jung},
title = {Absence of geodesics in first-passage percolation on a
half-plane},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 358-367},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855423}
}
Wehr, Jan; Woo, Jung. Absence of geodesics in first-passage percolation on a
half-plane. Ann. Probab., Tome 26 (1998) no. 1, pp. 358-367. http://gdmltest.u-ga.fr/item/1022855423/