We prove a complete pointwise ergodic theorem for Harris' basic one-dimensional two-sided nearest neighbor contact process, provided that the corresponding one-sided contact process is nonergodic.
@article{1176995154,
author = {Griffeath, David},
title = {Pointwise Ergodicity of the Basic Contact Process},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 139-142},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995154}
}
Griffeath, David. Pointwise Ergodicity of the Basic Contact Process. Ann. Probab., Tome 7 (1979) no. 6, pp. 139-142. http://gdmltest.u-ga.fr/item/1176995154/