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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: January 11, 2011
MathSciNet review: 2775794
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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: http://dx.doi.org/10.1090/S0002-9947-2011-05243-8
PII: S 0002-9947(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.