Faithful invariant random subgroups in acylindrically hyperbolic groups

Abstract

AbstractBuilding on work from Sun and Kechris‐Quorning, we prove that every acylindrically hyperbolic group admits a weakly mixing probability measure preserving action which is faithful but not essentially free. In other words, admits a weakly mixing nontrivial faithful IRS. We also prove that every nonelementary hyperbolic group admits a characteristic random subgroup with the same properties.