Some rigorous results for the Greenberg-Hastings Model
Publication
, Journal Article
Durrett, R; Steif, JE
Published in: Journal of Theoretical Probability
October 1, 1991
In this paper, we obtain some rigorous results for a cellular automaton known as the Greenberg-Hastings Model. The state space is {0, 1, 2}Zd. The dynamics are deterministic and discrete time. A site which is 1 changes to 2, a site which is 2 changes to 0, and a site which is 0 changes to a 1 if one of its 2 d neighbors is a 1. In one dimension, we compute the exact asymptotic rate at which the system dies out when started at random and compute the topological entropy. In two or more dimensions we show that starting from a nontrivial product measure, the limit exists as 3 m→∞ and is Bernoulli shift. Finally, we investigate the behavior of the system on a large finite box. © 1991 Plenum Publishing Corporation.
Duke Scholars
Published In
Journal of Theoretical Probability
DOI
EISSN
1572-9230
ISSN
0894-9840
Publication Date
October 1, 1991
Volume
4
Issue
4
Start / End Page
669 / 690
Related Subject Headings
- Statistics & Probability
- 0104 Statistics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Durrett, R., & Steif, J. E. (1991). Some rigorous results for the Greenberg-Hastings Model. Journal of Theoretical Probability, 4(4), 669–690. https://doi.org/10.1007/BF01259549
Durrett, R., and J. E. Steif. “Some rigorous results for the Greenberg-Hastings Model.” Journal of Theoretical Probability 4, no. 4 (October 1, 1991): 669–90. https://doi.org/10.1007/BF01259549.
Durrett R, Steif JE. Some rigorous results for the Greenberg-Hastings Model. Journal of Theoretical Probability. 1991 Oct 1;4(4):669–90.
Durrett, R., and J. E. Steif. “Some rigorous results for the Greenberg-Hastings Model.” Journal of Theoretical Probability, vol. 4, no. 4, Oct. 1991, pp. 669–90. Scopus, doi:10.1007/BF01259549.
Durrett R, Steif JE. Some rigorous results for the Greenberg-Hastings Model. Journal of Theoretical Probability. 1991 Oct 1;4(4):669–690.
Published In
Journal of Theoretical Probability
DOI
EISSN
1572-9230
ISSN
0894-9840
Publication Date
October 1, 1991
Volume
4
Issue
4
Start / End Page
669 / 690
Related Subject Headings
- Statistics & Probability
- 0104 Statistics
- 0101 Pure Mathematics