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A Complete Convergence Theorem for Attractive Reversible Nearest Particle Systems

Published online by Cambridge University Press:  20 November 2018

T. S. Mountford*
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA, USA 90024
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Abstract

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In this paper we prove a complete convergence theorem for attractive, reversible, super-critical nearest particle systems satisfying a natural regularity condition. In particular this implies that under these conditions there exist precisely two extremal invariant measures. The result we prove is relevant to question seven of Liggett (1985), Chapter VII.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

References

Bezuidenhout, C. and Grimmett, G., The critical contact process dies out, Ann. Probab. (4) 18(1990), 14621482.Google Scholar
Durrett, R., Oriented percolation in two dimensions, Ann. Probab. 12(1984), 999-1040.Google Scholar
Durrett, R., Lecture notes on particle systems and percolation processes, Wadsworth and Brooks/Cole, Pacific Grove, California, 1988.Google Scholar
Durrett, R., Lecture notes on particle systems and percolation processes, Wadsworth and Brooks/Cole, Pacific Grove, California, 1988.Google Scholar
Griffeath, D. and Liggett, T., Critical phenomena for Spitzer's reversible nearest-particle systems, Ann. Probab. 10(1982), 881895.Google Scholar
Mountford, T., Coupling of finite nearest particle systems, J. Appl. Probab. 30(1993), 258262.Google Scholar
Liggett, T., Attractive nearest particle systems, Ann. Probab. (1) 11(1983), 1633.Google Scholar
Liggett, T., Interacting particle systems, Springer, New York, 1985.Google Scholar