We consider a wide class of ergodic first passage percolation processes on ℤ2 and prove that there exist at least four one-sided geodesics a.s. We also show that coexistence is possible with positive probability in a four-color Richardson’s growth model. This improves earlier results of Häggström and Pemantle [J. Appl. Probab. 35 (1995) 683–692], Garet and Marchand [Ann. Appl. Probab. 15 (2005) 298–330] and Hoffman [Ann. Appl. Probab. 15 (2005) 739–747] who proved that first passage percolation has at least two geodesics and that coexistence is possible in a two-color Richardson’s growth model.
Publié le : 2008-10-15
Classification:
First passage percolation,
Richardson’s growth model,
60K35,
82B43
@article{1225372957,
author = {Hoffman, Christopher},
title = {Geodesics in first passage percolation},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 1944-1969},
language = {en},
url = {http://dml.mathdoc.fr/item/1225372957}
}
Hoffman, Christopher. Geodesics in first passage percolation. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 1944-1969. http://gdmltest.u-ga.fr/item/1225372957/