Approximation to uniform distribution in SO(3)

Damir Ferizović, Carlos Beltrán*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L 2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

Original languageEnglish
Pages (from-to)283-311
Number of pages29
JournalConstructive Approximation
Volume52
Issue number2
Early online date9 May 2020
DOIs
Publication statusPublished - 1 Oct 2020

Keywords

  • Determinantal point processes
  • Green energy
  • Point arrangements
  • Rotation group

ASJC Scopus subject areas

  • Computational Mathematics
  • Analysis
  • Mathematics(all)

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