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Bounded chaining in measurable dynamics
Abstract
We introduce a one-parameter family of notions between double ergodicity and metric ergodicity for measure-class preserving (i.e., nonsingular) actions of countable groups on standard probability spaces, providing infinitely many new invariants distinguishing weakly mixing actions. We call these properties (essentially) k-chaining, for k ∈ ℕ. We apply this framework to study boundary actions of free groups of finite rank r ≥ 1, where the boundary is equipped with a stationary Markov measure. We prove that in this context, weak mixing is equivalent to (2r−1)-chaining, as well as to strict irreducibility of the transition matrix of the Markov measure.
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BibTeX
@misc{tserunyan2026bounded,
title = {{Bounded chaining in measurable dynamics}},
author = {Anush Tserunyan and Jenna Zomback},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18061},
eprint = {2609.18061},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18061},
}
RIS
TY - UNPB
TI - Bounded chaining in measurable dynamics
AU - Anush Tserunyan
AU - Jenna Zomback
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.18061
UR - https://arxiv.org/abs/2609.18061
AB - We introduce a one-parameter family of notions between double ergodicity and metric ergodicity for measure-class preserving (i.e., nonsingular) actions of countable groups on standard probability spaces, providing infinitely many new invariants distinguishing weakly mixing actions. We call these properties (essentially) k-chaining, for k ∈ ℕ. We apply this framework to study boundary actions of free groups of finite rank r ≥ 1, where the boundary is equipped with a stationary Markov measure. We prove that in this context, weak mixing is equivalent to (2r−1)-chaining, as well as to strict irreducibility of the transition matrix of the Markov measure.
ER -