The intertwining property for $β$-Laguerre processes and integral operators for Jack polynomials
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915312006332416 |
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| author | Kawamato, Yosuke Shibukawa, Genki |
| author_facet | Kawamato, Yosuke Shibukawa, Genki |
| contents | The aim of this paper is to study intertwining relations for Laguerre process with inverse temperature $β\ge 1$ and parameter $α>-1$. We introduce a Markov kernel that depends on both $β$ and $ α$, and establish new intertwining relations for the $β$-Laguerre processes using this kernel. A key observation is that Jack symmetric polynomials are eigenfunctions of our Markov kernel, which allows us to apply a method established by Ramanan and Shkolnikov. Additionally, as a by-product, we derive an integral formula for multivariate Laguerre polynomials and multivariate hypergeometric functions associated with Jack polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23139 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The intertwining property for $β$-Laguerre processes and integral operators for Jack polynomials Kawamato, Yosuke Shibukawa, Genki Probability 60B20, 60J60 The aim of this paper is to study intertwining relations for Laguerre process with inverse temperature $β\ge 1$ and parameter $α>-1$. We introduce a Markov kernel that depends on both $β$ and $ α$, and establish new intertwining relations for the $β$-Laguerre processes using this kernel. A key observation is that Jack symmetric polynomials are eigenfunctions of our Markov kernel, which allows us to apply a method established by Ramanan and Shkolnikov. Additionally, as a by-product, we derive an integral formula for multivariate Laguerre polynomials and multivariate hypergeometric functions associated with Jack polynomials. |
| title | The intertwining property for $β$-Laguerre processes and integral operators for Jack polynomials |
| topic | Probability 60B20, 60J60 |
| url | https://arxiv.org/abs/2505.23139 |