Asymptotic expansion in measure and strong ergodicity
Li K, Vigolo F, Zhang J (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Pages Range: 1-39
DOI: 10.1142/S1793525321500278
Abstract
In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalizes expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterizing strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.
Authors with CRIS profile
Involved external institutions
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
Weizmann Institute of Science
Israel (IL)
University of Southampton
United Kingdom (GB)
Poland (PL)
Weizmann Institute of Science
Israel (IL)
University of Southampton
United Kingdom (GB)
How to cite
APA:
Li, K., Vigolo, F., & Zhang, J. (2021). Asymptotic expansion in measure and strong ergodicity. Journal of Topology and Analysis, 1-39. https://dx.doi.org/10.1142/S1793525321500278
MLA:
Li, Kang, Federico Vigolo, and Jiawen Zhang. "Asymptotic expansion in measure and strong ergodicity." Journal of Topology and Analysis (2021): 1-39.
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