Strong convergence for tensor GUE random matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910524345679872 |
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| author | Collins, Benoît Yuan, Wangjun |
| author_facet | Collins, Benoît Yuan, Wangjun |
| contents | Haagerup and Thorbjørnsen proved that iid GUEs converge strongly to free semicircular elements as the dimension grows to infinity. Motivated by considerations from quantum physics -- in particular, understanding nearest neighbor interactions in quantum spin systems -- we consider iid GUE acting on multipartite state spaces, with a mixing component on some sites and identity on the remaining sites. We show that under proper assumptions on the dimension of the sites, strong asymptotic freeness still holds. Our proof relies on an interpolation technology recently introduced by Bandeira, Boedihardjo and van Handel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09065 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong convergence for tensor GUE random matrices Collins, Benoît Yuan, Wangjun Probability Mathematical Physics Operator Algebras Haagerup and Thorbjørnsen proved that iid GUEs converge strongly to free semicircular elements as the dimension grows to infinity. Motivated by considerations from quantum physics -- in particular, understanding nearest neighbor interactions in quantum spin systems -- we consider iid GUE acting on multipartite state spaces, with a mixing component on some sites and identity on the remaining sites. We show that under proper assumptions on the dimension of the sites, strong asymptotic freeness still holds. Our proof relies on an interpolation technology recently introduced by Bandeira, Boedihardjo and van Handel. |
| title | Strong convergence for tensor GUE random matrices |
| topic | Probability Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2407.09065 |