Solvable Families of Random Block Tridiagonal Matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911685990678528 |
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| author | Rider, Brian Valkó, Benedek |
| author_facet | Rider, Brian Valkó, Benedek |
| contents | We introduce two families of random tridiagonal block matrices for which the joint eigenvalue distributions can be computed explicitly. These distributions are novel within random matrix theory, and exhibit interactions among eigenvalue coordinates beyond the typical mean-field log-gas type. Leveraging the matrix models, we go on to describe the point process limits at the edges of the spectrum in two ways: through certain random differential operators, and also in terms of coupled systems of diffusions. Along the way we establish several algebraic identities involving sums of Vandermonde determinant products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04579 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solvable Families of Random Block Tridiagonal Matrices Rider, Brian Valkó, Benedek Probability Mathematical Physics We introduce two families of random tridiagonal block matrices for which the joint eigenvalue distributions can be computed explicitly. These distributions are novel within random matrix theory, and exhibit interactions among eigenvalue coordinates beyond the typical mean-field log-gas type. Leveraging the matrix models, we go on to describe the point process limits at the edges of the spectrum in two ways: through certain random differential operators, and also in terms of coupled systems of diffusions. Along the way we establish several algebraic identities involving sums of Vandermonde determinant products. |
| title | Solvable Families of Random Block Tridiagonal Matrices |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2412.04579 |