Eigenstate thermalisation at the edge for Wigner matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912159358779392 |
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| author | Cipolloni, Giorgio Erdős, László Henheik, Joscha |
| author_facet | Cipolloni, Giorgio Erdős, László Henheik, Joscha |
| contents | We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is optimal for any observable. This complements earlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math., Sigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv: 2303.11142) that were restricted either to the bulk of the spectrum or to special observables. As a main ingredient, we prove a new multi-resolvent local law that optimally accounts for the edge scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05488 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eigenstate thermalisation at the edge for Wigner matrices Cipolloni, Giorgio Erdős, László Henheik, Joscha Probability Mathematical Physics 60B20, 82B10, 58J51 We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is optimal for any observable. This complements earlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math., Sigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv: 2303.11142) that were restricted either to the bulk of the spectrum or to special observables. As a main ingredient, we prove a new multi-resolvent local law that optimally accounts for the edge scaling. |
| title | Eigenstate thermalisation at the edge for Wigner matrices |
| topic | Probability Mathematical Physics 60B20, 82B10, 58J51 |
| url | https://arxiv.org/abs/2309.05488 |