Rising GUE Eigenvalue Process from a Fixed Level
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918475506647040 |
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| author | Himwich, Zoe |
| author_facet | Himwich, Zoe |
| contents | We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly as $\text{polylog}(m)$) to the extended semi-discrete sine kernel. As an application, we show fixed-energy universality of bulk local statistics of complex Hermitian Wigner matrices matching the covariance structure of GUE and with a finite $4+\varepsilon$ moment for $\varepsilon>0$. This application demonstrates that it is possible to obtain universality of bulk local statistics under near-optimal moment assumptions without using a Dyson Brownian motion relaxation step, which was a key ingredient in many results on this topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27619 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rising GUE Eigenvalue Process from a Fixed Level Himwich, Zoe Probability We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly as $\text{polylog}(m)$) to the extended semi-discrete sine kernel. As an application, we show fixed-energy universality of bulk local statistics of complex Hermitian Wigner matrices matching the covariance structure of GUE and with a finite $4+\varepsilon$ moment for $\varepsilon>0$. This application demonstrates that it is possible to obtain universality of bulk local statistics under near-optimal moment assumptions without using a Dyson Brownian motion relaxation step, which was a key ingredient in many results on this topic. |
| title | Rising GUE Eigenvalue Process from a Fixed Level |
| topic | Probability |
| url | https://arxiv.org/abs/2604.27619 |