Zihan Xia
Published 2022-12-12Version 1
We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups, decay of the isoperimetric profile for the essentially-free action is equivalent to amenability of the action in the sense of Zimmer. For measure-preserving actions, we find the bounds between the original and generalized isoperimetric profiles for measure-preserving actions.
Shadowing for actions of some finitely generated groups
The space of stable weak equivalence classes of measure-preserving actions
Equidistribution in measure-preserving actions of semisimple groups : case of $SL_2(\mathbb{R})$
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