On infinite-volume mixing

Details On infinite-volume mixing On infinite-volume mixing

2009-06-22

arxiv.org/abs/0906.4059v2

Comm. Math. Phys., 298 (2010), no. 2, 485-514

Mathematics

Dynamical Systems

34 pages, final version accepted by Communications in Mathematical Physics (some changes in Sect. 3 -- Prop. 3.1 in previous v

Scientific paper

10.1007/s00220-010-1043-6

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.

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