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arXiv · 1211.1284

A coupling construction for spin systems with infinite range interactions

François Ezanno
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Abstract

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has already been widely used since the interacting particle systems were introduced, but our construction brings a new insight to understand why it is natural. The process is first constructed as a limit of finite spin systems. Then we identify its generator and give a simple criterion for a measure to be invariant with respect to it.

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François Ezanno. 2012-11-06. A coupling construction for spin systems with infinite range interactions. https://arxiv.org/abs/1211.1284

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