The Binary Contact Path Process
Griffeath, David
Ann. Probab., Tome 11 (1983) no. 4, p. 692-705 / Harvested from Project Euclid
We study some $\{0, 1, \cdots\}^{z^d}$ valued Markov interactions $\eta_t$ called contact path processes. These are similar to branching random walks, in that the normalized size process starting from a singleton is a martingale which converges to a limit $M_\infty$. In contrast to branching, however, $M_\infty$ depends on the spatial dynamics of the path process. The main result is an exact evaluation of the variance of $M_\infty$, achieved by means of the Feynman-Kac formula. The basic contact process of Harris may be viewed as a projection of $\eta_t$; as a corollary to the main result we obtain bounds on the contact process critical value $\lambda^{(d)}_c$ in dimension $d \geq 3$.
Publié le : 1983-08-14
Classification:  Contact processes,  interacting particle systems,  critical values,  phase transition,  Feynman-Kac formula,  60K35
@article{1176993514,
     author = {Griffeath, David},
     title = {The Binary Contact Path Process},
     journal = {Ann. Probab.},
     volume = {11},
     number = {4},
     year = {1983},
     pages = { 692-705},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993514}
}
Griffeath, David. The Binary Contact Path Process. Ann. Probab., Tome 11 (1983) no. 4, pp.  692-705. http://gdmltest.u-ga.fr/item/1176993514/