On infinite-volume mixing
Dynamical Systems
2010-07-27 v2
Abstract
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be relevant, at least for extended systems with a direct physical interpretation. We discuss the pros and cons of a few mathematical definitions that can be devised, testing them on a prototypical class of infinite measure-preserving dynamical systems, namely, the random walks.
Cite
@article{arxiv.0906.4059,
title = {On infinite-volume mixing},
author = {Marco Lenci},
journal= {arXiv preprint arXiv:0906.4059},
year = {2010}
}
Comments
34 pages, final version accepted by Communications in Mathematical Physics (some changes in Sect. 3 -- Prop. 3.1 in previous version was partially incorrect)