Log-concavity and concentration bounds for a single gap between GUE eigenvalues
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912810597875712 |
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| author | Johnston, Samuel G. G. |
| author_facet | Johnston, Samuel G. G. |
| contents | We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to prove several concentration bounds for the semicircle-renormalised eigengaps, improving on bounds recently obtained in [Tao (2024). On the distribution of eigenvalues of GUE and its minors at fixed index. [arXiv:2412.10889]]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04869 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-concavity and concentration bounds for a single gap between GUE eigenvalues Johnston, Samuel G. G. Probability 60B20, 52A40, 60G15 We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to prove several concentration bounds for the semicircle-renormalised eigengaps, improving on bounds recently obtained in [Tao (2024). On the distribution of eigenvalues of GUE and its minors at fixed index. [arXiv:2412.10889]]. |
| title | Log-concavity and concentration bounds for a single gap between GUE eigenvalues |
| topic | Probability 60B20, 52A40, 60G15 |
| url | https://arxiv.org/abs/2601.04869 |