Multiple collisions of eigenvalues and singular values of matrix Gaussian field
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913428071776256 |
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| author | Yuan, Wangjun |
| author_facet | Yuan, Wangjun |
| contents | Let $X^β$ be a real symmetric or complex Hermitian matrix whose entries are independent Gaussian random fields. We provide the sufficient and necessary conditions such that multiple collisions of eigenvalue processes of $A^β+ T_βX^βT_β^*$ occur with positive probability. In addition, for a real or complex rectangular matrix $W^β$ with independent Gaussian random field entries, we obtain the sufficient and necessary conditions under which the probability of multiple collisions of non-trivial singular value processes of $B^β+ T_βW^β\tilde T_β$ is positive. In both cases, the size of the set of collision times is characterized via Hausdorff dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple collisions of eigenvalues and singular values of matrix Gaussian field Yuan, Wangjun Probability Let $X^β$ be a real symmetric or complex Hermitian matrix whose entries are independent Gaussian random fields. We provide the sufficient and necessary conditions such that multiple collisions of eigenvalue processes of $A^β+ T_βX^βT_β^*$ occur with positive probability. In addition, for a real or complex rectangular matrix $W^β$ with independent Gaussian random field entries, we obtain the sufficient and necessary conditions under which the probability of multiple collisions of non-trivial singular value processes of $B^β+ T_βW^β\tilde T_β$ is positive. In both cases, the size of the set of collision times is characterized via Hausdorff dimension. |
| title | Multiple collisions of eigenvalues and singular values of matrix Gaussian field |
| topic | Probability |
| url | https://arxiv.org/abs/2407.09070 |