Fluctuations in Quantum Unique Ergodicity at the Spectral Edge
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915546972291072 |
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| author | Benigni, Lucas Chen, Nixia Lopatto, Patrick Xie, Xiaoyu |
| author_facet | Benigni, Lucas Chen, Nixia Lopatto, Patrick Xie, Xiaoyu |
| contents | We study the eigenvector mass distribution of an $N\times N$ Wigner matrix on a set of coordinates $I$ satisfying $| I | \ge c N$ for some constant $c >0$. For eigenvectors corresponding to eigenvalues at the spectral edge, we show that the sum of the mass on these coordinates converges to a Gaussian in the $N \rightarrow \infty$ limit, after a suitable rescaling and centering. The proof proceeds by a two moment matching argument. We directly compare edge eigenvector observables of an arbitrary Wigner matrix to those of a Gaussian matrix, which may be computed explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11142 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fluctuations in Quantum Unique Ergodicity at the Spectral Edge Benigni, Lucas Chen, Nixia Lopatto, Patrick Xie, Xiaoyu Probability Mathematical Physics We study the eigenvector mass distribution of an $N\times N$ Wigner matrix on a set of coordinates $I$ satisfying $| I | \ge c N$ for some constant $c >0$. For eigenvectors corresponding to eigenvalues at the spectral edge, we show that the sum of the mass on these coordinates converges to a Gaussian in the $N \rightarrow \infty$ limit, after a suitable rescaling and centering. The proof proceeds by a two moment matching argument. We directly compare edge eigenvector observables of an arbitrary Wigner matrix to those of a Gaussian matrix, which may be computed explicitly. |
| title | Fluctuations in Quantum Unique Ergodicity at the Spectral Edge |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2303.11142 |