Zeros Of Random Analytic Functions And Spectral Properties Of Perturbed Unitary Matrices
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911136782221312 |
|---|---|
| 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 |