Universality of extremal eigenvalues of large random matrices
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866911443898597376 |
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| author | Cipolloni, Giorgio Erdős, László Xu, Yuanyuan |
| author_facet | Cipolloni, Giorgio Erdős, László Xu, Yuanyuan |
| contents | We prove that the spectral radius of a large random matrix $X$ with independent, identically distributed complex entries follows the Gumbel law irrespective of the distribution of the matrix elements. This solves a long-standing conjecture of Bordenave and Chafa{\"ı} and it establishes the first universality result for one of the most prominent extremal spectral statistics in random matrix theory. Furthermore, we also prove that the argument of the largest eigenvalue is uniform on the unit circle and that the extremal eigenvalues of $X$ form a Poisson point process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08325 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universality of extremal eigenvalues of large random matrices Cipolloni, Giorgio Erdős, László Xu, Yuanyuan Probability Mathematical Physics 60B20, 60G55, 60G70 We prove that the spectral radius of a large random matrix $X$ with independent, identically distributed complex entries follows the Gumbel law irrespective of the distribution of the matrix elements. This solves a long-standing conjecture of Bordenave and Chafa{\"ı} and it establishes the first universality result for one of the most prominent extremal spectral statistics in random matrix theory. Furthermore, we also prove that the argument of the largest eigenvalue is uniform on the unit circle and that the extremal eigenvalues of $X$ form a Poisson point process. |
| title | Universality of extremal eigenvalues of large random matrices |
| topic | Probability Mathematical Physics 60B20, 60G55, 60G70 |
| url | https://arxiv.org/abs/2312.08325 |