  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.
