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On Infinite-Volume Mixing

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

    Marco Lenci

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  1. Marco Lenci
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Correspondence to Marco Lenci.

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Communicated by G. Gallavotti

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Lenci, M. On Infinite-Volume Mixing. Commun. Math. Phys. 298, 485–514 (2010). https://doi.org/10.1007/s00220-010-1043-6

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