Minimization of the Probabilistic p-frame Potential
Functional Analysis
2017-09-04 v2 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1101.0140,
title = {Minimization of the Probabilistic p-frame Potential},
author = {Martin Ehler and Kasso A. Okoudjou},
journal= {arXiv preprint arXiv:1101.0140},
year = {2017}
}