On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912726567092224 |
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| author | Dai, Dan Lu, Chenhao |
| author_facet | Dai, Dan Lu, Chenhao |
| contents | In this paper, we prove an optimal global rigidity estimate for the eigenvalues of the Jacobi unitary ensemble. Our approach begins by constructing a random measure defined through the eigenvalue counting function. We then prove its convergence to a Gaussian multiplicative chaos measure, which leads to the desired rigidity result. To establish this convergence, we apply a sufficient condition from Claeys et al. \cite{CFL2021} and conduct an asymptotic analysis of the related exponential moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble Dai, Dan Lu, Chenhao Probability Mathematical Physics In this paper, we prove an optimal global rigidity estimate for the eigenvalues of the Jacobi unitary ensemble. Our approach begins by constructing a random measure defined through the eigenvalue counting function. We then prove its convergence to a Gaussian multiplicative chaos measure, which leads to the desired rigidity result. To establish this convergence, we apply a sufficient condition from Claeys et al. \cite{CFL2021} and conduct an asymptotic analysis of the related exponential moments. |
| title | On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2511.18967 |