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Minimization of the Probabilistic p-frame Potential

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arxiv 1101.0140 v2 pith:3VHYOYA6 submitted 2010-12-30 math.FA math.STstat.TH

Martin Ehler , Kasso A. Okoudjou This is my paper · ORCID
classification math.FAmath.STstat.TH
keywords optimalconfigurationsprobabilisticcharacterizedistributionsframepointspotential
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We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory. Furthermore, we consider similar optimal configurations in terms of random distributions of points on the sphere. In this probabilistic setting, we characterize these optimal distributions by means of special classes of probabilistic frames. Our work also indicates some connections between statistical shape analysis and frame theory.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal measures for p-frame energies on spheres

    math.MG 2019-08 accept novelty 8.0 of 10

    Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].

  2. Energy on spheres and discreteness of minimizing measures

    math.CA 2019-08 conditional novelty 7.0 of 10

    For non-even p, every minimizer of the p-frame energy on the sphere has support with empty interior, and for potentials with finitely many positive Gegenbauer coefficients a discrete minimizer always exists.

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