Free probability of type B prime
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912082337726464 |
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| author | Fujie, Katsunori Hasebe, Takahiro |
| author_facet | Fujie, Katsunori Hasebe, Takahiro |
| contents | Free probability of type B was invented by Biane--Goodman--Nica, and then it was generalized by Belinschi--Shlyakhtenko and Février--Nica to infinitesimal free probability. The latter found its applications to eigenvalues of perturbed random matrices in the work of Shlyakhtenko and Cébron--Dahlqvist--Gabriel. This paper offers a new framework, called ``free probability of type B${}^\prime$'', which appears in the large size limit of independent unitarily invariant random matrices with perturbations. Our framework is related to boolean, free, (anti)monotone, cyclic-(anti)monotone and conditionally free independences. We then apply the new framework to the principal minor of unitarily invariant random matrices, which leads to the definition of a multivariate inverse Markov--Krein transform. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_14582 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Free probability of type B prime Fujie, Katsunori Hasebe, Takahiro Operator Algebras Probability 46L54, 60B20 Free probability of type B was invented by Biane--Goodman--Nica, and then it was generalized by Belinschi--Shlyakhtenko and Février--Nica to infinitesimal free probability. The latter found its applications to eigenvalues of perturbed random matrices in the work of Shlyakhtenko and Cébron--Dahlqvist--Gabriel. This paper offers a new framework, called ``free probability of type B${}^\prime$'', which appears in the large size limit of independent unitarily invariant random matrices with perturbations. Our framework is related to boolean, free, (anti)monotone, cyclic-(anti)monotone and conditionally free independences. We then apply the new framework to the principal minor of unitarily invariant random matrices, which leads to the definition of a multivariate inverse Markov--Krein transform. |
| title | Free probability of type B prime |
| topic | Operator Algebras Probability 46L54, 60B20 |
| url | https://arxiv.org/abs/2310.14582 |