The Diamond ensemble: A constructive set of spherical points with small logarithmic energy

Maria de Ujue Etayo Rodriguez; Carlos Beltran

doi:10.1016/j.jco.2020.101471

The Diamond ensemble: A constructive set of spherical points with small logarithmic energy

Maria de Ujue Etayo Rodriguez^*, Carlos Beltran

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We define a family of random sets of points, the Diamond ensemble, on the sphere S2 depending on several parameters. Its most important property is that, for some of these parameters, the asymptotic expected value of the logarithmic energy of the points can be computed rigorously and shown to attain very small values, quite close to the conjectured minimal value.

Original language	English
Article number	101471
Number of pages	22
Journal	Journal of Complexity
Volume	59
DOIs	https://doi.org/10.1016/j.jco.2020.101471
Publication status	Published - Aug 2020

Keywords

Constructive spherical points
Minimal logarithmic energy

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics
Mathematics(all)
Numerical Analysis
Algebra and Number Theory
Statistics and Probability

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10.1016/j.jco.2020.101471

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title = "The Diamond ensemble: A constructive set of spherical points with small logarithmic energy",

abstract = "We define a family of random sets of points, the Diamond ensemble, on the sphere S2 depending on several parameters. Its most important property is that, for some of these parameters, the asymptotic expected value of the logarithmic energy of the points can be computed rigorously and shown to attain very small values, quite close to the conjectured minimal value.",

keywords = "Constructive spherical points, Minimal logarithmic energy",

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AU - Beltran, Carlos

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AB - We define a family of random sets of points, the Diamond ensemble, on the sphere S2 depending on several parameters. Its most important property is that, for some of these parameters, the asymptotic expected value of the logarithmic energy of the points can be computed rigorously and shown to attain very small values, quite close to the conjectured minimal value.

KW - Constructive spherical points

KW - Minimal logarithmic energy

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U2 - 10.1016/j.jco.2020.101471

DO - 10.1016/j.jco.2020.101471

M3 - Article

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VL - 59

JO - Journal of Complexity

JF - Journal of Complexity

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ER -

The Diamond ensemble: A constructive set of spherical points with small logarithmic energy

Abstract

Keywords

ASJC Scopus subject areas

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