Asymptotic expansion in measure and strong ergodicity

Li K, Vigolo F, Zhang J (2021)

Publication Type: Journal article

Publication year: 2021


Pages Range: 1-39

DOI: 10.1142/S1793525321500278


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.

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Li, K., Vigolo, F., & Zhang, J. (2021). Asymptotic expansion in measure and strong ergodicity. Journal of Topology and Analysis, 1-39.


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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