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Proceedings of the American Mathematical Society

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Distribution of point charges with small discrete energy

Author: Igor E. Pritsker
Journal: Proc. Amer. Math. Soc. 139 (2011), 3461-3473
MSC (2010): Primary 31C20; Secondary 31C15
Published electronically: May 18, 2011
MathSciNet review: 2813378
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Abstract: We study the asymptotic equidistribution of points near arbitrary compact sets of positive capacity in $ \mathbb{R}^d, d\ge 2$. Our main tools are the energy estimates for Riesz potentials. We also consider the quantitative aspects of this equidistribution in the classical Newtonian case. In particular, we quantify the weak convergence of discrete measures to the equilibrium measure and give the estimates of convergence rates for discrete potentials to the equilibrium potential.

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Igor E. Pritsker
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078

Keywords: Riesz potentials, Newton potentials, equilibrium measure, discrete energy, Fekete points, minimum energy, discrepancy.
Received by editor(s): January 8, 2010
Published electronically: May 18, 2011
Additional Notes: The author’s research was partially supported by the National Security Agency and by the Alexander von Humboldt Foundation.
Communicated by: Mario Bonk
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.