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arXiv · 1911.08272

A topological dynamical system with two different positive sofic entropies

Dylan Airey·Lewis Bowen·Frank Lin
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Abstract

A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic entropy theory is a generalization of classical entropy theory in dynamics to actions by sofic groups. However, the sofic entropy of an action may depend on a choice of sofic approximation. All previously known examples showing this dependence rely on degenerate behavior. This paper exhibits an explicit example of a mixing subshift of finite type with two different positive sofic entropies. The example is inspired by statistical physics literature on 2-colorings of random hyper-graphs.

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Dylan Airey, Lewis Bowen, Frank Lin. 2019-11-19. A topological dynamical system with two different positive sofic entropies. https://arxiv.org/abs/1911.08272

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