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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/2507.07310 |
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| _version_ | 1866911048460664832 |
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| author | Tapias, Diego Grüger, Benedikt Kühn, Reimer Sollich, Peter |
| author_facet | Tapias, Diego Grüger, Benedikt Kühn, Reimer Sollich, Peter |
| contents | The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity equations, has been successful in identifying the top eigenvalue when the associated eigenvector is extended. However, this approach fails when the eigenvector is localized. In this work, we adapt the real-valued cavity method to address this limitation by introducing a novel criterion that exploits the constraints of the cavity equations to detect the top eigenvalue in systems with a localized top eigenvector. Our results are validated using the Anderson model as a paradigmatic example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization and top eigenvalue detection Tapias, Diego Grüger, Benedikt Kühn, Reimer Sollich, Peter Disordered Systems and Neural Networks Statistical Mechanics The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity equations, has been successful in identifying the top eigenvalue when the associated eigenvector is extended. However, this approach fails when the eigenvector is localized. In this work, we adapt the real-valued cavity method to address this limitation by introducing a novel criterion that exploits the constraints of the cavity equations to detect the top eigenvalue in systems with a localized top eigenvector. Our results are validated using the Anderson model as a paradigmatic example. |
| title | Localization and top eigenvalue detection |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2507.07310 |