$q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911307369807872 |
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| author | Kimura, Taro |
| author_facet | Kimura, Taro |
| contents | We study $q$-deformation of probability measures on partitions, i.e., $q$-deformed random partitions. We in particular consider the $q$-Plancherel measure and show a determinantal formula for the correlation function using a $q$-deformation of the discrete Bessel kernel. We also investigate Riemann-Hilbert problems associated with the corresponding orthogonal polynomials and obtain $q$-Painlevé equations from the $q$-difference Lax formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem Kimura, Taro Combinatorics Mathematical Physics Probability We study $q$-deformation of probability measures on partitions, i.e., $q$-deformed random partitions. We in particular consider the $q$-Plancherel measure and show a determinantal formula for the correlation function using a $q$-deformation of the discrete Bessel kernel. We also investigate Riemann-Hilbert problems associated with the corresponding orthogonal polynomials and obtain $q$-Painlevé equations from the $q$-difference Lax formalism. |
| title | $q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem |
| topic | Combinatorics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2503.00766 |