Abstract
We establish conditions for survival and extinction of types of one-dimensional voter models, and show that increasing the flip rates at a finite number of sites typically does not affect survival, unless the flipping mechanism is altered. We provide an example of a modified voter model that does not survive but can be made to survive simply by altering the flip mechanism at one site. We also show that a rather general class of such models have clustering behavior.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Handjani, S. (1999). Spatial perturbations of one-dimensional spin systems. Stochastic Process. Appl. 81, 73–79.
Hoel, P., Port, S., and Stone, C. (1972). Introduction to Stochastic Processes, Houghton Mifflin Company, Boston.
Liggett, T. M. (1985). Interacting Particle Systems, Springer, New York.
Madras, N., Schinazi, R., and Schonmann, R. (1994). On the critical behavior of the contact process in deterministic inhomogeneous environment. Ann. Probab. 22, 1140–1159.
Spitzer, F. (1976). Principles of Random Walk, 2nd. ed., Springer-Verlag, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Handjani, S.J. Inhomogeneous Voter Models in One Dimension. Journal of Theoretical Probability 16, 325–338 (2003). https://doi.org/10.1023/A:1023562309007
Issue Date:
DOI: https://doi.org/10.1023/A:1023562309007