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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Cornell University Library, arXiv.org
22.08.2024
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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. |
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| 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 |
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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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| Title | On the logarithmic energy of solutions to the polynomial eigenvalue problem |
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