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• W3104284520 abstract "Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, we establish the amenability of all subgroups of the group IET of interval exchange transformations that have angular components of rational rank~${leq 2}$. In addition, we obtain a reformulation of extensive amenability in terms of inverted orbits and use it to present a purely probabilistic proof that recurrent actions are extensively amenable. Finally, we study the triviality of the Poisson boundary for random walks on IET and show that there are subgroups $G <IET$ admitting no finitely supported measure with trivial boundary." @default.
• W3104284520 created "2020-11-23" @default.
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• W3104284520 date "2016-07-29" @default.
• W3104284520 modified "2023-10-12" @default.
• W3104284520 title "Extensive amenability and an application to interval exchanges" @default.
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• W3104284520 doi "https://doi.org/10.1017/etds.2016.32" @default.
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