Mixing and tight polyhedra
Abstract
Actions of by automorphisms of compact zero-dimensional groups exhibit a range of mixing behaviour. Schmidt introduced the notion of mixing shapes for these systems, and proved that non-mixing shapes can only arise non-trivially for actions on zero-dimensional groups. Masser has shown that the failure of higher-order mixing is always witnessed by non-mixing shapes. Here we show how valuations can be used to understand the (non-)mixing behaviour of a certain family of examples. The sharpest information arises for systems corresponding to tight polyhedra.
Cite
@article{arxiv.math/0503569,
title = {Mixing and tight polyhedra},
author = {Thomas Ward},
journal= {arXiv preprint arXiv:math/0503569},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/074921706000000194 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)