On the logarithmic energy of solutions to the polynomial eigenvalue problem

• Published in: arXiv.org
• Main Authors: Armentano, Diego, Carrasco, Federico, Fiori, Marcelo
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 22.08.2024
• Subjects: Eigenvalues; Logarithms; Polynomials

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...