External Fields and Uniform Distribution in Squares and Cubes

Research output: Contribution to conferencePoster


Points in the unit cube in Rd that maximize, say, the sum of all mutual Euclidean distances, or minimize, say, their potential energy (harmonic kernel), are located at the boundary of the unit cube. This phenomenon is a consequence of classical potential theory. We introduce suitable external fields to obtain a uniform distribution over the unit cube of optimal configurations for
the corresponding "energy functional".
Original languageEnglish
Number of pages1
Publication statusPublished - 11 Sep 2019
EventHDA2019: 8th Workshop on High-Dimensional Approximation - ETH Zurich, Zurich, Switzerland
Duration: 9 Sep 201913 Sep 2019


WorkshopHDA2019: 8th Workshop on High-Dimensional Approximation
Abbreviated titleHDA 2019
Internet address

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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