On the distribution of eigenvalues of GUE and its minors at fixed index
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915063803150336 |
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| author | Tao, Terence |
| author_facet | Tao, Terence |
| contents | We obtain bounds on the distribution of normalized gaps of eigenvalues of $N \times N$ GUE matrix in the bulk, that do not lose logarithmic factors of $N$ in the limit $N \to \infty$. As an application, we obtain fixed index universality results for the GUE minor process, which in turn are useful for establishing limiting results for random hives with GUE boundary data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the distribution of eigenvalues of GUE and its minors at fixed index Tao, Terence Probability 60B20 We obtain bounds on the distribution of normalized gaps of eigenvalues of $N \times N$ GUE matrix in the bulk, that do not lose logarithmic factors of $N$ in the limit $N \to \infty$. As an application, we obtain fixed index universality results for the GUE minor process, which in turn are useful for establishing limiting results for random hives with GUE boundary data. |
| title | On the distribution of eigenvalues of GUE and its minors at fixed index |
| topic | Probability 60B20 |
| url | https://arxiv.org/abs/2412.10889 |