Uniquely ergodic tilings of amenable groups
Fundamenta Mathematicae
MSC: Primary 37A15; Secondary 28D15, 37A35, 37B10, 37C85
DOI: 10.4064/fm240323-14-3
Published online: 11 July 2025
Abstract
For a countable amenable group $G$, we prove the existence of a uniquely ergodic zero entropy tiling of $G$, whose tiles have arbitrarily good invariance properties. This improves the tiling construction of Downarowicz, Huczek and Zhang (2019) by adding unique ergodicity.
