Subgroup mixing and random walks in groups acting on hyperbolic spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909451937644544 |
|---|---|
| author | Hull, M. Minasyan, A. Osin, D. |
| author_facet | Hull, M. Minasyan, A. Osin, D. |
| contents | 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 which allow us to extend some results on random walks of Abbott and the first author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subgroup mixing and random walks in groups acting on hyperbolic spaces Hull, M. Minasyan, A. Osin, D. Group Theory 20F65, 20F67 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 which allow us to extend some results on random walks of Abbott and the first author. |
| title | Subgroup mixing and random walks in groups acting on hyperbolic spaces |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2407.16069 |