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arXiv · 2208.11624

Faithful invariant random subgroups in acylindrically hyperbolic groups

Yair Glasner·Anton Hase
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Abstract

Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group $G$ admits a weakly mixing probability measure preserving action $G \curvearrowright (X,\mathcal{B},\mu)$ which is faithful but not essentially free. In other words, $G$ admits a weakly mixing nontrivial faithful IRS. We also prove that every non-elementary hyperbolic group admits a characteristic random subgroup with the same properties.

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Yair Glasner, Anton Hase. 2022-08-24. Faithful invariant random subgroups in acylindrically hyperbolic groups. https://arxiv.org/abs/2208.11624

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