Fixation Results for Threshold Voter Systems
Durrett, Richard ; Steif, Jeffrey E.
Ann. Probab., Tome 21 (1993) no. 4, p. 232-247 / Harvested from Project Euclid
We consider threshold voter systems in which the threshold $\tau > n/2$, where $n$ is the number of neighbors, and we present results in support of the following picture of what happens starting from product measure with density $1/2$. The system fixates, that is, each site flips only finitely many times. There is a critical value, $\theta_c$, so that if $\tau = \theta n$ with $\theta > \theta_c$ and $n$ is large then most sites never flip, while for $\theta \in (1/2, \theta_c)$ and $n$ large, the limiting state consists mostly of large regions of points of the same type. In $d = 1, \theta_c \approx 0.6469076$ while in $d > 1, \theta_c = 3/4$.
Publié le : 1993-01-14
Classification:  Cellular automata,  large deviations,  voter models,  60K35
@article{1176989403,
     author = {Durrett, Richard and Steif, Jeffrey E.},
     title = {Fixation Results for Threshold Voter Systems},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 232-247},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989403}
}
Durrett, Richard; Steif, Jeffrey E. Fixation Results for Threshold Voter Systems. Ann. Probab., Tome 21 (1993) no. 4, pp.  232-247. http://gdmltest.u-ga.fr/item/1176989403/