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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.03252 |
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| _version_ | 1866911136782221312 |
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| author | Fares, Aniss |
| author_facet | Fares, Aniss |
| contents | We study the spectral properties of a rank-one multiplicative perturbation of a unitary matrix, a model introduced by Fyodorov. Building upon earlier results by Forrester and Ipsen, we provide a direct proof that the eigenvalues converge to the zeros of a specific Gaussian analytic function. Our approach extends these results to other unitarily invariant models. This method enables us to address a question raised by Dubach and Reker concerning the critical timescale at which an outlier emerges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zeros Of Random Analytic Functions And Spectral Properties Of Perturbed Unitary Matrices Fares, Aniss Probability 60B20, 30B20, 15B52 (Primary) 47B93 (Secondary) We study the spectral properties of a rank-one multiplicative perturbation of a unitary matrix, a model introduced by Fyodorov. Building upon earlier results by Forrester and Ipsen, we provide a direct proof that the eigenvalues converge to the zeros of a specific Gaussian analytic function. Our approach extends these results to other unitarily invariant models. This method enables us to address a question raised by Dubach and Reker concerning the critical timescale at which an outlier emerges. |
| title | Zeros Of Random Analytic Functions And Spectral Properties Of Perturbed Unitary Matrices |
| topic | Probability 60B20, 30B20, 15B52 (Primary) 47B93 (Secondary) |
| url | https://arxiv.org/abs/2509.03252 |