Stable orbit equivalence of Bernoulli actions of free groups and   isomorphism of some of their factor actions
  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 \Gamma of n infinite amenable groups, the factor K^{\Gamma}/K of the Bernoulli action of \Gamma on K^{\Gamma} by the diagonal action of K, is isomorphic with a Bernoulli action of \Gamma. 
Niels Meesschaert, Sven Raum and Stefaan Vaes
math.OA math.DS math.GR