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arXiv · 2311.17580

Scaling entropy growth gap

Georgii Veprev
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Abstract

The scaling entropy of a p.m.p. action is a slow-entropy type invariant that characterizes the intermediate growth of entropy in a dynamical system. An amenable group $G$ has a scaling entropy growth gap if the scaling entropy of any its free p.m.p. action admits a non-trivial lower bound. We prove that the group $S_\infty$ of all finite permutations has a scaling entropy growth gap as well as the Houghton group $\mathcal{H}_2$. By proving this, we show that there are finitely generated amenable groups with this property.

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Georgii Veprev. 2023-11-29. Scaling entropy growth gap. https://arxiv.org/abs/2311.17580

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