Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929517707132928 |
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| author | Popa, M. Szpojankowski, K. Tseng, P. -L. |
| author_facet | Popa, M. Szpojankowski, K. Tseng, P. -L. |
| contents | We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE matrix has a null infinitesimal distribution. Moreover, we show that asymptotically different permutations of the same GUE matrix are infinitesimally free. Besides this we study particular example of entry permutation - the transpose, and we show that while a GUE matrix is asymptotically free from its transpose it is not infinitesimally free from it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07434 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness Popa, M. Szpojankowski, K. Tseng, P. -L. Probability Combinatorics Operator Algebras 46L54, 15A52, 05A99 We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE matrix has a null infinitesimal distribution. Moreover, we show that asymptotically different permutations of the same GUE matrix are infinitesimally free. Besides this we study particular example of entry permutation - the transpose, and we show that while a GUE matrix is asymptotically free from its transpose it is not infinitesimally free from it. |
| title | Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness |
| topic | Probability Combinatorics Operator Algebras 46L54, 15A52, 05A99 |
| url | https://arxiv.org/abs/2210.07434 |