Concentration of invariant means and dynamics of chain stabilizers in continuous geometries
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913210372718592 |
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| author | Schneider, Friedrich Martin |
| author_facet | Schneider, Friedrich Martin |
| contents | We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann's continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_09427 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Concentration of invariant means and dynamics of chain stabilizers in continuous geometries Schneider, Friedrich Martin Functional Analysis Group Theory Rings and Algebras 22A10, 43A07, 06C20, 16E50 We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann's continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups. |
| title | Concentration of invariant means and dynamics of chain stabilizers in continuous geometries |
| topic | Functional Analysis Group Theory Rings and Algebras 22A10, 43A07, 06C20, 16E50 |
| url | https://arxiv.org/abs/2204.09427 |