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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.11708 |
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| _version_ | 1866909777107353600 |
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| author | Demni, Nizar Hamdi, Tarek |
| author_facet | Demni, Nizar Hamdi, Tarek |
| contents | We compute the large size limit of the moment formula derived in \cite{DHS} for the Hermitian Jacobi process at fixed time. Our computations rely on the polynomial division algorithm which allows to obtain cancellations similar to those obtained in Lemma 3 in \cite{Bia}. In particular, we identify the terms contributing to the limit and show they satisfy a double recurrence relation. We also determine explicitly some of them and revisit a special case relying on Carlitz summation identity for terminating $1$-balanced ${}_4F_3$ functions taken at unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments of the free Jacobi process: a matrix approach Demni, Nizar Hamdi, Tarek Probability Combinatorics Operator Algebras 46L54, 15B52, 60B20, 33C80 We compute the large size limit of the moment formula derived in \cite{DHS} for the Hermitian Jacobi process at fixed time. Our computations rely on the polynomial division algorithm which allows to obtain cancellations similar to those obtained in Lemma 3 in \cite{Bia}. In particular, we identify the terms contributing to the limit and show they satisfy a double recurrence relation. We also determine explicitly some of them and revisit a special case relying on Carlitz summation identity for terminating $1$-balanced ${}_4F_3$ functions taken at unity. |
| title | Moments of the free Jacobi process: a matrix approach |
| topic | Probability Combinatorics Operator Algebras 46L54, 15B52, 60B20, 33C80 |
| url | https://arxiv.org/abs/2404.11708 |