Eigenvalue degeneracy in sparse random matrices
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911510982295552 |
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| author | Shimura, Masanari |
| author_facet | Shimura, Masanari |
| contents | In random matrices with independent and continuous matrix entries, the degeneracy probability of the eigenvalues is known to be zero. In this paper, random matrices including discontinuous matrix entries are analyzed in order to observe how degeneracy is generated. Using Erdös-Rényi matching probability theory of random bipartite graphs, we asymptotically evaluate the degeneracy probability of such random matrices. As a result, due to accumulation of the eigenvalues to the origin, a positive degeneracy probability is found for eigenvalues of a sparse random matrix model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11105 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenvalue degeneracy in sparse random matrices Shimura, Masanari Mathematical Physics Probability 60B20, 05C80 In random matrices with independent and continuous matrix entries, the degeneracy probability of the eigenvalues is known to be zero. In this paper, random matrices including discontinuous matrix entries are analyzed in order to observe how degeneracy is generated. Using Erdös-Rényi matching probability theory of random bipartite graphs, we asymptotically evaluate the degeneracy probability of such random matrices. As a result, due to accumulation of the eigenvalues to the origin, a positive degeneracy probability is found for eigenvalues of a sparse random matrix model. |
| title | Eigenvalue degeneracy in sparse random matrices |
| topic | Mathematical Physics Probability 60B20, 05C80 |
| url | https://arxiv.org/abs/2601.11105 |