The extremal landscape for the C$β$E ensemble
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917812768866304 |
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| author | Paquette, Elliot Zeitouni, Ofer |
| author_facet | Paquette, Elliot Zeitouni, Ofer |
| contents | We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$β$E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) towards the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a "derivative martingale". We also provide a description of the landscape near extrema points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_06743 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The extremal landscape for the C$β$E ensemble Paquette, Elliot Zeitouni, Ofer Probability We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$β$E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) towards the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a "derivative martingale". We also provide a description of the landscape near extrema points. |
| title | The extremal landscape for the C$β$E ensemble |
| topic | Probability |
| url | https://arxiv.org/abs/2209.06743 |