Approximation to uniform distribution in SO(3)

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URI: http://hdl.handle.net/10902/20786
ISSN: 0176-4276
ISSN: 1432-0940
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Autoría
Beltrán Álvarez, CarlosAutoridad Unican; Ferizovc, Damir
Fecha
2020-05
Derechos
©Springer New York . This is a post-peer-review, pre-copyedit version of an article published in Constructive Approximation. The final authenticated version is available online at: https://doi.org/10.1007/s00365-020-09506-1
Publicado en
Constructive Approximation volume 52, pages283-311(2020)
Editorial
Springer-Verl. New York.
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Palabras clave
Rotation group
Point arrangements
Green energy
Determinantal point processes
Resumen/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
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