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# A complete convergence theorem for attractive reversible nearest particle systems

Published:1997-04-01
Printed: Apr 1997
• T. S. Mountford
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## Abstract

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.