On the logarithmic energy of solutions to the polynomial eigenvalue problem
In this paper, we compute the expected logarithmic energy of solutions to the polynomial eigenvalue problem for random matrices. We generalize some known results for the Shub-Smale polynomials, and the spherical ensemble. These two processes are the two extremal particular cases of the polynomial ei...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
20.08.2024
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| Online Access | Get full text |
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| Abstract | In this paper, we compute the expected logarithmic energy of solutions to the
polynomial eigenvalue problem for random matrices. We generalize some known
results for the Shub-Smale polynomials, and the spherical ensemble. These two
processes are the two extremal particular cases of the polynomial eigenvalue
problem, and we prove that the logarithmic energy lies between these two cases.
In particular, the roots of the Shub-Smale polynomials are the ones with the
lowest logarithmic energy of the family. |
|---|---|
| AbstractList | In this paper, we compute the expected logarithmic energy of solutions to the
polynomial eigenvalue problem for random matrices. We generalize some known
results for the Shub-Smale polynomials, and the spherical ensemble. These two
processes are the two extremal particular cases of the polynomial eigenvalue
problem, and we prove that the logarithmic energy lies between these two cases.
In particular, the roots of the Shub-Smale polynomials are the ones with the
lowest logarithmic energy of the family. |
| Author | Carrasco, Federico Fiori, Marcelo Armentano, Diego |
| Author_xml | – sequence: 1 givenname: Diego surname: Armentano fullname: Armentano, Diego – sequence: 2 givenname: Federico surname: Carrasco fullname: Carrasco, Federico – sequence: 3 givenname: Marcelo surname: Fiori fullname: Fiori, Marcelo |
| BackLink | https://doi.org/10.48550/arXiv.2408.11148$$DView paper in arXiv |
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| DOI | 10.48550/arxiv.2408.11148 |
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| Snippet | In this paper, we compute the expected logarithmic energy of solutions to the
polynomial eigenvalue problem for random matrices. We generalize some known... |
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| SubjectTerms | Computer Science - Numerical Analysis Mathematics - Numerical Analysis Mathematics - Probability |
| Title | On the logarithmic energy of solutions to the polynomial eigenvalue problem |
| URI | https://arxiv.org/abs/2408.11148 |
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