The Stolarsky Principle and Energy Optimization on the Sphere

Dmitriy Bilyk, Feng Dai, Ryan Matzke

Type: Article

Publication Date: 2018-01-09

Citations: 28

DOI: https://doi.org/10.1007/s00365-017-9412-4

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Constructive Approximation - View
arXiv (Cornell University) - View - PDF

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+	Numerical integration on graphs: Where to sample and how to weigh	2019	George C. Linderman Stefan Steinerberger
+ PDF Chat	Maximizing expected powers of the angle between pairs of points in projective space	2022	Tongseok Lim Robert J. McCann
+	Stolarsky’s invariance principle for projective spaces	2019	M. M. Skriganov
+ PDF Chat	Permutation $p$-value approximation via generalized Stolarsky invariance	2018	Hera Y. He Kinjal Basu Qingyuan Zhao Art B. Owen
+	Geodesic distance Riesz energy on the sphere	2018	Dmitriy Bilyk Chang‐Feng Dai
+ PDF Chat	Single radius spherical cap discrepancy via gegenbadly approximable numbers	2024	Dmitriy Bilyk Michelle Mastrianni Stefan Steinerberger
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+	Stolarsky's invariance principle for finite metric spaces	2020	Alexander Barg
+ PDF Chat	Bounds for the sum of distances of spherical sets of small size	2023	Alexander Barg Peter Boyvalenkov Maya Stoyanova
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Works Cited by This (26)

Action	Title	Year	Authors
+ PDF Chat	Asymptotics for minimal discrete energy on the sphere	1998	Arno B. J. Kuijlaars E. B. Saff
+ PDF Chat	Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets	2007	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+ PDF Chat	Spherical distributions of $N$ points with maximal distance sums are well spaced	1975	Kenneth B. Stolarsky
+	Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry	1984	József Beck
+ PDF Chat	Sums of Distances Between Points on a Sphere	1972	Kenneth B. Stolarsky
+	Slice discrepancy and irregularities of distribution on spheres	1991	Martin Blümlinger
+	Some extremal problems for positive definite sequences and related extremal convex conformal maps of the circle	1958	I. J. Schoenberg
+ PDF Chat	Solution of a gemetric problem by Fejes Tóth.	1962	H. Larcher
+ PDF Chat	Reformulation of the covering and quantizer problems as ground states of interacting particles	2010	Salvatore Torquato
+	About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case	2006	Johann S. Brauchart