Singularity degree of structured random matrices
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916467502481408 |
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| author | Krüger, Torben Renfrew, David |
| author_facet | Krüger, Torben Renfrew, David |
| contents | We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up, which we label the singularity degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_08811 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Singularity degree of structured random matrices Krüger, Torben Renfrew, David Probability Mathematical Physics Functional Analysis 60B20, 15B52, 46Txx We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up, which we label the singularity degree. |
| title | Singularity degree of structured random matrices |
| topic | Probability Mathematical Physics Functional Analysis 60B20, 15B52, 46Txx |
| url | https://arxiv.org/abs/2108.08811 |