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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.18427 |
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| _version_ | 1866912942485667840 |
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| author | Claeys, Tom Zhang, Jiyuan |
| author_facet | Claeys, Tom Zhang, Jiyuan |
| contents | In this paper, we prove that biorthogonal ensembles on the real line with a specific derivative structure admit an explicit correlation kernel of double contour integral form. We will demonstrate that this expression is a valuable starting point for asymptotic analysis and that our class of biorthogonal ensembles admits a large variety of limit kernels, by proving that two new classes of limit kernels can occur. The first type is a deformation of the hard edge Bessel kernel which arises in polynomial ensembles describing the eigenvalues of the sum of two random matrices, while the second type arises for Muttalib-Borodin type deformations of polynomial ensembles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18427 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Biorthogonal ensembles of derivative type Claeys, Tom Zhang, Jiyuan Mathematical Physics Probability 60G55, 60B20, 42C05, 30E10 In this paper, we prove that biorthogonal ensembles on the real line with a specific derivative structure admit an explicit correlation kernel of double contour integral form. We will demonstrate that this expression is a valuable starting point for asymptotic analysis and that our class of biorthogonal ensembles admits a large variety of limit kernels, by proving that two new classes of limit kernels can occur. The first type is a deformation of the hard edge Bessel kernel which arises in polynomial ensembles describing the eigenvalues of the sum of two random matrices, while the second type arises for Muttalib-Borodin type deformations of polynomial ensembles. |
| title | Biorthogonal ensembles of derivative type |
| topic | Mathematical Physics Probability 60G55, 60B20, 42C05, 30E10 |
| url | https://arxiv.org/abs/2601.18427 |