The extremal landscape for the C $\beta $ E ensemble
We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C $\beta $ E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) toward the sum of a Gumbel variable and another independent variable, which we cha...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001294/type/journal_article |
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| author | Elliot Paquette Ofer Zeitouni |
| author_facet | Elliot Paquette Ofer Zeitouni |
| author_sort | Elliot Paquette |
| collection | DOAJ |
| description | We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C
$\beta $
E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) toward 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 | Article |
| id | doaj-art-a1b95f1a928f468eb1cfc481b8473bac |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-a1b95f1a928f468eb1cfc481b8473bac2025-01-16T21:48:28ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.129The extremal landscape for the C $\beta $ E ensembleElliot Paquette0https://orcid.org/0000-0003-4156-6687Ofer Zeitouni1https://orcid.org/0000-0002-2520-1525Department of Mathematics and Statistics, McGill University, Burnside Hall 925, 805 Sherbrooke Street West, Montreal, Quebec H3A 0B9, Canada; E-mail:Department of Mathematics, Weizmann Institute, 207 Herzl Street, Rehovot 76100, IsraelWe consider the extremes of the logarithm of the characteristic polynomial of matrices from the C $\beta $ E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) toward 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.https://www.cambridge.org/core/product/identifier/S2050509424001294/type/journal_article15A5260G70 |
| spellingShingle | Elliot Paquette Ofer Zeitouni The extremal landscape for the C $\beta $ E ensemble Forum of Mathematics, Sigma 15A52 60G70 |
| title | The extremal landscape for the C $\beta $ E ensemble |
| title_full | The extremal landscape for the C $\beta $ E ensemble |
| title_fullStr | The extremal landscape for the C $\beta $ E ensemble |
| title_full_unstemmed | The extremal landscape for the C $\beta $ E ensemble |
| title_short | The extremal landscape for the C $\beta $ E ensemble |
| title_sort | extremal landscape for the c beta e ensemble |
| topic | 15A52 60G70 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001294/type/journal_article |
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