Convergence of local eigenvector processes of generalized Wigner matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914053681577984 |
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| author | Benigni, Lucas Feyzabady, Mohammadreza Rezaei |
| author_facet | Benigni, Lucas Feyzabady, Mohammadreza Rezaei |
| contents | We prove convergence of eigenvector processes of the form $(\sqrt{N}\langle \mathbf{u}_k,A_t\mathbf{u}_k\rangle)_{t\in[0,1]}$ where $\mathbf{u}_k$ is a bulk eigenvector of generalized Wigner matrices and $(A_t)$ a family of symmetric matrices with bounded norm and Hölder regularity. We give explicit examples of limiting processes and prove that a large class of Gaussian process with Hölder-continuous covariance function can be obtained as such a limit using its Karhunen--Loève expansion. The proof is based on the multi-dimensional convergence proved Benigni and Cipolloni (2024) and a tightness criterion proved using Hölder regularity of the observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of local eigenvector processes of generalized Wigner matrices Benigni, Lucas Feyzabady, Mohammadreza Rezaei Probability We prove convergence of eigenvector processes of the form $(\sqrt{N}\langle \mathbf{u}_k,A_t\mathbf{u}_k\rangle)_{t\in[0,1]}$ where $\mathbf{u}_k$ is a bulk eigenvector of generalized Wigner matrices and $(A_t)$ a family of symmetric matrices with bounded norm and Hölder regularity. We give explicit examples of limiting processes and prove that a large class of Gaussian process with Hölder-continuous covariance function can be obtained as such a limit using its Karhunen--Loève expansion. The proof is based on the multi-dimensional convergence proved Benigni and Cipolloni (2024) and a tightness criterion proved using Hölder regularity of the observables. |
| title | Convergence of local eigenvector processes of generalized Wigner matrices |
| topic | Probability |
| url | https://arxiv.org/abs/2509.19581 |