Localization of One-Dimensional Random Band Matrices
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914010307231744 |
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| author | Drogin, Reuben |
| author_facet | Drogin, Reuben |
| contents | We consider a general class of $n\times n$ random band matrices with bandwidth $W$. When $W^2\ll n$, we prove that with high probability the eigenvectors of such matrices are localized and decay exponentially at the sharp scale $W^2$. Combined with the delocalization results of Yau and Yin [arXiv:2501.01718] and of Erdős and Riabov [arXiv:2506.06441], this establishes the conjectured localization-delocalization transition for a large class of random band matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization of One-Dimensional Random Band Matrices Drogin, Reuben Probability Mathematical Physics We consider a general class of $n\times n$ random band matrices with bandwidth $W$. When $W^2\ll n$, we prove that with high probability the eigenvectors of such matrices are localized and decay exponentially at the sharp scale $W^2$. Combined with the delocalization results of Yau and Yin [arXiv:2501.01718] and of Erdős and Riabov [arXiv:2506.06441], this establishes the conjectured localization-delocalization transition for a large class of random band matrices. |
| title | Localization of One-Dimensional Random Band Matrices |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2508.05802 |