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Minimizing the discrete logarithmic energy on the sphere: The role of random polynomials

Abstract: We prove that points in the sphere associated with roots of random polynomials via the stereographic projection are surprisingly well-suited with respect to the minimal logarithmic energy on the sphere. That is, roots of random polynomials provide a fairly good approximation to elliptic Fekete points.

 Authorship: Armentano D., BeltrAn C., Shub M.,

 Fuente: Transactions of the American Mathematical Society 363 (2011), 2955-2965

 Publisher: American Mathematical Society

 Year of publication: 2011

 No. of pages: 11

 Publication type: Article

 DOI: 10.1090/S0002-9947-2011-05243-8

 ISSN: 0002-9947,1088-6850

 Publication Url: https://doi.org/10.1090/S0002-9947-2011-05243-8

Authorship

ARMENTANO, DIEGO

SHUB, MICHAEL