The intertwining property for Laguerre processes with a fixed parameter
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911800833867776 |
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| author | Bufetov, Alexander I. Kawamoto, Yosuke |
| author_facet | Bufetov, Alexander I. Kawamoto, Yosuke |
| contents | We investigate the intertwining of Laguerre processes of parameter $α$ in different dimensions.
We introduce a Feller kernel that depends on $α$ and intertwines the $α$-Laguerre process in $N+1$ dimensions and that in $N$ dimensions.
When $α$ is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order $(N+α+1) \times (N+1)$ are fixed, then the those of its $(N+α) \times N $ truncation matrix are given by the new kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The intertwining property for Laguerre processes with a fixed parameter Bufetov, Alexander I. Kawamoto, Yosuke Probability Mathematical Physics Dynamical Systems We investigate the intertwining of Laguerre processes of parameter $α$ in different dimensions. We introduce a Feller kernel that depends on $α$ and intertwines the $α$-Laguerre process in $N+1$ dimensions and that in $N$ dimensions. When $α$ is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order $(N+α+1) \times (N+1)$ are fixed, then the those of its $(N+α) \times N $ truncation matrix are given by the new kernel. |
| title | The intertwining property for Laguerre processes with a fixed parameter |
| topic | Probability Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2403.11718 |