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January, 1993 Fixation Results for Threshold Voter Systems
Richard Durrett, Jeffrey E. Steif
Ann. Probab. 21(1): 232-247 (January, 1993). DOI: 10.1214/aop/1176989403


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 $d > 1, \theta_c = 3/4$.


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Richard Durrett. Jeffrey E. Steif. "Fixation Results for Threshold Voter Systems." Ann. Probab. 21 (1) 232 - 247, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0769.60092
MathSciNet: MR1207225
Digital Object Identifier: 10.1214/aop/1176989403

Primary: 60K35

Keywords: cellular automata , large deviations , voter models

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 1 • January, 1993
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