Extensive amenability and an application to interval exchanges

Kate Juschenko, Nicolás Matte Bon, Nicolas Monod, Mikael De La Salle

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 of interval exchange transformations that have angular components of rational rank less than or equal to two. 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 and show that there are subgroups <![CDATA[$G admitting no finitely supported measure with trivial boundary.

Original languageEnglish (US)
Pages (from-to)195-219
Number of pages25
JournalErgodic Theory and Dynamical Systems
Volume38
Issue number1
DOIs
StatePublished - Feb 1 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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