Sobolev convergence of log-determinants for smooth Wigner matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911724338151424 |
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| author | Cipolloni, Giorgio Lopatto, Patrick |
| author_facet | Cipolloni, Giorgio Lopatto, Patrick |
| contents | We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically correlated, random elements in every negative Sobolev space $H^{-s}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27222 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sobolev convergence of log-determinants for smooth Wigner matrices Cipolloni, Giorgio Lopatto, Patrick Probability Mathematical Physics We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically correlated, random elements in every negative Sobolev space $H^{-s}$. |
| title | Sobolev convergence of log-determinants for smooth Wigner matrices |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2605.27222 |