Minimization of the Probabilistic p-frame Potential

Abstract

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.

References in corpus (2)

• Random Tight Frames
• Frame theory in directional statistics

Cited by in corpus (19)

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• Moments of isotropic measures and optimal projective codes
• Repeated minimizers of $p$-frame energies
• Potential theory with multivariate kernels
• Scalable Probabilistic Frames
• Preconditioning filter bank decompositions using structured normalized tight frames
• Null dimension witness based on single measurements
• Uniform tight frames as optimal signals
• Optimal properties of the canonical tight probabilistic frame
• Gradient Flows for Frame Potentials on the Wasserstein Space
• p-adic Welch Bounds and p-adic Zauner Conjecture
• On the Search for Tight Frames of Low Coherence
• Identify Equivalent Frames
• Fusion frames and randomized subspace actions