Hyperlinear approximations to amenable groups come from sofic approximations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911754394533888 |
|---|---|
| author | Burton, Peter Chaudkhari, Maksym Juschenko, Kate Muliarchyk, Kyrylo |
| author_facet | Burton, Peter Chaudkhari, Maksym Juschenko, Kate Muliarchyk, Kyrylo |
| contents | We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a group is simulated by a suitable sofic approximation. The proof is probabilistic, using the concentration of measure in high-dimensional spheres to control the deviation of an operator's matrix coefficients from its trace. As a corollary, we obtain a result connecting stability of sofic approximations with stability of hyperlinear approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09202 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperlinear approximations to amenable groups come from sofic approximations Burton, Peter Chaudkhari, Maksym Juschenko, Kate Muliarchyk, Kyrylo Group Theory We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a group is simulated by a suitable sofic approximation. The proof is probabilistic, using the concentration of measure in high-dimensional spheres to control the deviation of an operator's matrix coefficients from its trace. As a corollary, we obtain a result connecting stability of sofic approximations with stability of hyperlinear approximations. |
| title | Hyperlinear approximations to amenable groups come from sofic approximations |
| topic | Group Theory |
| url | https://arxiv.org/abs/2311.09202 |