English

Faithful invariant random subgroups in acylindrically hyperbolic groups

Group Theory 2022-08-25 v1 Dynamical Systems

Abstract

Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group GG admits a weakly mixing probability measure preserving action G(X,B,μ)G \curvearrowright (X,\mathcal{B},\mu) which is faithful but not essentially free. In other words, GG 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.

Cite

@article{arxiv.2208.11624,
  title  = {Faithful invariant random subgroups in acylindrically hyperbolic groups},
  author = {Yair Glasner and Anton Hase},
  journal= {arXiv preprint arXiv:2208.11624},
  year   = {2022}
}

Comments

14 pages, 1 figure

R2 v1 2026-06-25T01:56:28.719Z