Polish Models and Sofic Entropy
Abstract
For actions of a sofic group on probability spaces, the entropy has been defined by Bowen, with an extension by Kerr-Li. In particular, when the action is by homeomorphisms of a compact space preserving a given measure, Kerr-Li show one can compute the measure-theoretic entropy in a manner which uses the topology of the space. We show how to compute the entropy of a an action of homeomorphisms of a Polish space preserving a given measure, also in a manner which uses the topology of the space. We give applications to spectral properties of actions with positive entropy, as well as for actions of completely positive entropy.
Cite
@article{arxiv.1411.1510,
title = {Polish Models and Sofic Entropy},
author = {Ben Hayes},
journal= {arXiv preprint arXiv:1411.1510},
year = {2016}
}
Comments
26 pages. Removed the section on distal actions as we will prove more general results in "Mixing and Spectral Gap Relative to Pinsker Factors for Sofic Groups". This is the final version to appear in Journal of Institute of Mathematics of Jussieu