Random commuting matrices
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910941718773760 |
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| author | McCarthy, John E. |
| author_facet | McCarthy, John E. |
| contents | We define a random commuting $d$-tuple of $n$-by-$n$ matrices to be a random variable that takes values in the set of commuting $d$-tuples and has a distribution that is a rapidly decaying continuous weight on this algebraic set. In the Hermitian case, we characterize the eigenvalue distribution as $n$ tends to infinity. In the non-Hermitian case, we get a formula that holds if the set is irreducible. We show that there are qualitative differences between the single matrix case and the several commuting matrices case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_20029 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random commuting matrices McCarthy, John E. Probability Functional Analysis 60B20, 15B22 We define a random commuting $d$-tuple of $n$-by-$n$ matrices to be a random variable that takes values in the set of commuting $d$-tuples and has a distribution that is a rapidly decaying continuous weight on this algebraic set. In the Hermitian case, we characterize the eigenvalue distribution as $n$ tends to infinity. In the non-Hermitian case, we get a formula that holds if the set is irreducible. We show that there are qualitative differences between the single matrix case and the several commuting matrices case. |
| title | Random commuting matrices |
| topic | Probability Functional Analysis 60B20, 15B22 |
| url | https://arxiv.org/abs/2305.20029 |