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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
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
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 321 - 337
Copyright
Copyright © Canadian Mathematical Society 1997

References

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