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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.10222 |
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| _version_ | 1866915540091535360 |
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| author | Becker, Simon Oltman, Izak Vogel, Martin |
| author_facet | Becker, Simon Oltman, Izak Vogel, Martin |
| contents | If $A \colon D(A) \subset \mathcal{H} \to \mathcal{H}$ is an unbounded Fredholm operator of index $0$ on a Hilbert space $\mathcal{H}$ with a dense domain $D(A)$, then its spectrum is either discrete or the entire complex plane. This spectral dichotomy plays a central role in the study of magic angles in twisted bilayer graphene. This paper proves that if such operators (with certain additional assumptions) are perturbed by certain random trace-class operators, their spectrum is discrete with high probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Instability of Random Fredholm Operators Becker, Simon Oltman, Izak Vogel, Martin Spectral Theory Mathematical Physics If $A \colon D(A) \subset \mathcal{H} \to \mathcal{H}$ is an unbounded Fredholm operator of index $0$ on a Hilbert space $\mathcal{H}$ with a dense domain $D(A)$, then its spectrum is either discrete or the entire complex plane. This spectral dichotomy plays a central role in the study of magic angles in twisted bilayer graphene. This paper proves that if such operators (with certain additional assumptions) are perturbed by certain random trace-class operators, their spectrum is discrete with high probability. |
| title | Spectral Instability of Random Fredholm Operators |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2502.10222 |