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arXiv · 1907.04814

Discrepancy of minimal Riesz energy points

Jordi Marzo·Albert Mas
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Abstract

We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz $s$-energy on the sphere $\mathbb S^d.$ Our results are based in bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in $\mathbb S^2$ were obtained. Our result improves previously known bounds for $0\le s<2$ and $s\neq 1$ in $\mathbb S^2,$ where $s=0$ is Wolff's result, and for $d-t_0<s<d$ with $t_0\approx 2.5$ when $d\ge 3$ and $s\neq d-1.$

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Jordi Marzo, Albert Mas. 2019-07-10. Discrepancy of minimal Riesz energy points. https://arxiv.org/abs/1907.04814

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