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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.19454 |
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| _version_ | 1866915505588142080 |
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| author | Grabowski, Łukasz Jardón-Sánchez, Héctor Mellick, Sam |
| author_facet | Grabowski, Łukasz Jardón-Sánchez, Héctor Mellick, Sam |
| contents | Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem, and extend it both to locally compact second countable groups and unimodular random graphs. We prove unimodular random graph analogues of the Connes--Weiss and Glasner--Weiss theorem characterising Property (T). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unimodular random graphs with Property (T) have cost one Grabowski, Łukasz Jardón-Sánchez, Héctor Mellick, Sam Group Theory Dynamical Systems Probability Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem, and extend it both to locally compact second countable groups and unimodular random graphs. We prove unimodular random graph analogues of the Connes--Weiss and Glasner--Weiss theorem characterising Property (T). |
| title | Unimodular random graphs with Property (T) have cost one |
| topic | Group Theory Dynamical Systems Probability |
| url | https://arxiv.org/abs/2506.19454 |