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

Authors:
Diego Armentano, Carlos Beltrán and Michael Shub

Journal:
Trans. Amer. Math. Soc. **363** (2011), 2955-2965

MSC (2010):
Primary 31C20, 52A40, 60J45; Secondary 65Y20

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

Published electronically:
January 11, 2011

MathSciNet review:
2775794

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Diego Armentano**

Affiliation:
Centro de Matemática, Universidad de la República, Montevideo, Uruguay

Email:
diego@cmat.edu.uy

**Carlos Beltrán**

Affiliation:
Departmento de Matemáticas, Universidad de Cantabria, Santander, Spain

Email:
carlos.beltran@unican.es

**Michael Shub**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada

Address at time of publication:
CONICET, Departmento de Matemáticas, Universidad de Buenos Aires, Buenos Aires, Argentina

Email:
shub.michael@gmail.com

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

Keywords:
Logarithmic energy,
elliptic Fekete points,
random polynomials

Received by editor(s):
January 12, 2009

Published electronically:
January 11, 2011

Additional Notes:
The first author was partially supported by CSIC, Uruguay

The second author was partially suported by the research project MTM2007-62799 from the Spanish Ministry of Science MICINN

The third author was partially supported by an NSERC grant

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.