Central Limit Theorem for Tensor Products of Free Variables via Bi-Free Independence
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909212867559424 |
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| author | Skoufranis, Paul |
| author_facet | Skoufranis, Paul |
| contents | In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of certain self-adjoint quantum channels and tensor products of random matrices tend to a distribution that can be obtained by an averaged sum of products of bi-freely independent pairs. Subsequently, using bi-free techniques, a Central Limit Theorem for such operator is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Central Limit Theorem for Tensor Products of Free Variables via Bi-Free Independence Skoufranis, Paul Operator Algebras 46L53, 46L54 In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of certain self-adjoint quantum channels and tensor products of random matrices tend to a distribution that can be obtained by an averaged sum of products of bi-freely independent pairs. Subsequently, using bi-free techniques, a Central Limit Theorem for such operator is established. |
| title | Central Limit Theorem for Tensor Products of Free Variables via Bi-Free Independence |
| topic | Operator Algebras 46L53, 46L54 |
| url | https://arxiv.org/abs/2405.19216 |