Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions

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Abstract

We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and every free product Γ of infinite amenable groups, the factor Γ{right curved arrow}KΓ/K of the Bernoulli action Γ{right curved arrow}KΓ by the diagonal K-action is isomorphic with a Bernoulli action of Γ. © 2012 Elsevier Ltd.

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Meesschaert, N., Raum, S., & Vaes, S. (2013). Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions. Expositiones Mathematicae, 31(3), 274–294. https://doi.org/10.1016/j.exmath.2012.08.012

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