On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations

Abstract

We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and consider their relation to other notions of mixing in infinite measure.

Some typos corrected, a reference added, arguments expanded

References in corpus (2)

• Rational weak mixing in infinite measure spaces
• Law of large numbers for certain cylinder flows

Cited by in corpus (2)

• Conditions for rational weak mixing
• Symmetric Birkhoff sums in infinite ergodic theory