Subgroup mixing and random walks in groups acting on hyperbolic spaces
Subgroup mixing and random walks in groups acting on hyperbolic spaces
We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure μ, random walks with respect to μ will produce elements with strong mixing properties for this action asymptotically almost surely. In particular, when the group has no finite normal subgroups, this implies that the action is highly topologically transitive. Along the way, we prove technical results about convex cocompact subgroups that allow us to extend some results on random walks of Abbott and the first author.
group actions, topological dynamics, topological transitivity, μ-mixing
Hull, Michael
fcc213e1-3dd7-4c40-809f-e499d3f421a0
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Osin, Denis
32a9932c-f439-4b83-b639-1a53ac6bf6f5
22 May 2026
Hull, Michael
fcc213e1-3dd7-4c40-809f-e499d3f421a0
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Osin, Denis
32a9932c-f439-4b83-b639-1a53ac6bf6f5
Hull, Michael, Minasyan, Ashot and Osin, Denis
(2026)
Subgroup mixing and random walks in groups acting on hyperbolic spaces.
Ergodic Theory and Dynamical Systems.
(doi:10.1017/etds.2026.10310).
Abstract
We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure μ, random walks with respect to μ will produce elements with strong mixing properties for this action asymptotically almost surely. In particular, when the group has no finite normal subgroups, this implies that the action is highly topologically transitive. Along the way, we prove technical results about convex cocompact subgroups that allow us to extend some results on random walks of Abbott and the first author.
Text
Subgroup_mixing_and_random_walks-Apr_22-2026
- Accepted Manuscript
Text
subgroup-mixing-and-random-walks-in-groups-acting-on-hyperbolic-spaces
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e-pub ahead of print date: 22 May 2026
Published date: 22 May 2026
Keywords:
group actions, topological dynamics, topological transitivity, μ-mixing
Identifiers
Local EPrints ID: 512076
URI: http://eprints.soton.ac.uk/id/eprint/512076
ISSN: 0143-3857
PURE UUID: c4b5f181-c3eb-468a-94a9-8e07ce1253c6
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Date deposited: 16 Jun 2026 16:30
Last modified: 19 Aug 2026 02:25
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Contributors
Author:
Michael Hull
Author:
Denis Osin
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