Dynamics of a rank-one multiplicative perturbation of a unitary matrix
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911355741667328 |
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| author | Dubach, Guillaume Reker, Jana |
| author_facet | Dubach, Guillaume Reker, Jana |
| contents | We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on $U$ that hold for a variety of unitary random matrix models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14638 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dynamics of a rank-one multiplicative perturbation of a unitary matrix Dubach, Guillaume Reker, Jana Probability Mathematical Physics 60B20, 15B52 (Primary) 47B93 (Secondary) We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on $U$ that hold for a variety of unitary random matrix models. |
| title | Dynamics of a rank-one multiplicative perturbation of a unitary matrix |
| topic | Probability Mathematical Physics 60B20, 15B52 (Primary) 47B93 (Secondary) |
| url | https://arxiv.org/abs/2212.14638 |