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东金文 《中国科学A辑(英文版)》2001,44(11):1373-1380
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple
proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov
processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding
stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal
ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain
extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and
the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal
invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our
results provide partial answers to certain interesting problems in spin systems. 相似文献
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