Local variational principle concerning entropy of a sofic group action
Abstract
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any finite open cover of the space, and show that these local measure-theoretic and topological entropy coincide with their classical counterparts when the acting group is an infinite amenable group.
Cite
@article{arxiv.1109.3244,
title = {Local variational principle concerning entropy of a sofic group action},
author = {Guo Hua Zhang},
journal= {arXiv preprint arXiv:1109.3244},
year = {2011}
}