We consider the model of random interlacements on ℤd introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in u of the probability that the origin belongs to the infinite component of the vacant set at level u in the supercritical phase u*.
Publié le : 2009-02-15
Classification:
Random walks,
percolation,
random interlacements,
60K35,
82C41
@article{1235140345,
author = {Teixeira, Augusto},
title = {On the uniqueness of the infinite cluster of the vacant set of random interlacements},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 454-466},
language = {en},
url = {http://dml.mathdoc.fr/item/1235140345}
}
Teixeira, Augusto. On the uniqueness of the infinite cluster of the vacant set of random interlacements. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 454-466. http://gdmltest.u-ga.fr/item/1235140345/