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Approximation to uniform distribution in SO(3)

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 L2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest

 Fuente: Constructive Approximation volume 52, pages 283-311(2020)

Editorial: Springer-Verl. New York.

 Fecha de publicación: 01/05/2020

Nº de páginas: 29

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00365-020-09506-1

ISSN: 0176-4276,1432-0940

 Proyecto español: MTM2017-83816-P

Url de la publicación: https://doi.org/10.1007/s00365-020-09506-1