We study the threshold θ contact process on ℤd with infection parameter λ. We show that the critical point λc, defined as the threshold for survival starting from every site occupied, vanishes as d→∞. This implies that the threshold θ voter model on ℤd has a nondegenerate extremal invariant measure, when d is large.
Publié le : 2009-07-15
Classification:
Threshold contact process,
threshold voter model,
critical points,
invariant measures,
large dimensions,
60K35
@article{1248182145,
author = {Mountford, Thomas and Schonmann, Roberto H.},
title = {The survival of large dimensional threshold contact processes},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 1483-1501},
language = {en},
url = {http://dml.mathdoc.fr/item/1248182145}
}
Mountford, Thomas; Schonmann, Roberto H. The survival of large dimensional threshold contact processes. Ann. Probab., Tome 37 (2009) no. 1, pp. 1483-1501. http://gdmltest.u-ga.fr/item/1248182145/