Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916351850840064 |
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| author | Bourgade, Paul Lopatto, Patrick Zeitouni, Ofer |
| author_facet | Bourgade, Paul Lopatto, Patrick Zeitouni, Ofer |
| contents | We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and $β$-ensembles. In the special case of Gaussian-divisible Wigner matrices, our method provides universality of the maximum up to tightness. These are the first universal results on the Fyodorov--Hiary--Keating conjectures for these models, and in particular answer the question of optimal rigidity for the spectrum of Wigner matrices.
Our proofs combine dynamical techniques for universality of eigenvalue statistics with ideas surrounding the maxima of log-correlated fields and Gaussian multiplicative chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13335 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices Bourgade, Paul Lopatto, Patrick Zeitouni, Ofer Probability Mathematical Physics We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and $β$-ensembles. In the special case of Gaussian-divisible Wigner matrices, our method provides universality of the maximum up to tightness. These are the first universal results on the Fyodorov--Hiary--Keating conjectures for these models, and in particular answer the question of optimal rigidity for the spectrum of Wigner matrices. Our proofs combine dynamical techniques for universality of eigenvalue statistics with ideas surrounding the maxima of log-correlated fields and Gaussian multiplicative chaos. |
| title | Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2312.13335 |