On infinite-volume mixing
arXiv:0906.4059 · doi:10.1007/s00220-010-1043-6
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.
34 pages, final version accepted by Communications in Mathematical Physics (some changes in Sect. 3 -- Prop. 3.1 in previous version was partially incorrect)
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Cited by in corpus (17)
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