arXiv:1705.08559 Abstract | arXiv Analytics

arXiv:1705.08559 [math.DS]Abstract References Reviews Resources

Random ordering formula for sofic and Rokhlin entropy of Gibbs measures

Published 2017-05-23Version 1

We prove the explicit formula for sofic and Rokhlin entropy of actions arising from some class of Gibbs measures. It provides a new set of examples with sofic entropy independent of sofic approximations. It is particularilly interresting, since in non-amenable case Rokhlin entropy was computed only in case of Bernoulli actions and for some examples with zero Rokhlin entropy. As an example we show that our formula holds for the supercritical Ising model. We also establish a criterion for uniqueness of Gibbs measure by means of f-invariant.

Comments: 23 pages

Categories: math.DS, math.PR

Keywords: gibbs measure, random ordering formula, non-amenable case rokhlin entropy, sofic entropy independent, zero rokhlin entropy

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