A topological dynamical system with two different positive sofic entropies
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.
Cite
@article{arxiv.1911.08272,
title = {A topological dynamical system with two different positive sofic entropies},
author = {Dylan Airey and Lewis Bowen and Frank Lin},
journal= {arXiv preprint arXiv:1911.08272},
year = {2021}
}
Comments
This new version corrects a number of minor errors in the previous version