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arXiv · 2506.13388

Points on $\operatorname{SO}(3)$ with low logarithmic energy

Carlos Beltrán·Federico Carrasco·Damir Ferizović·Pedro R. López-Gómez
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Abstract

We describe several randomized collections of $3\times 3$ rotation matrices and analyze their associated logarithmic energy. The best one (i.e. the one attaining the lowest expected logarithmic energy) is constructed by choosing $r$ spherical points, which come from the zeros of a randomly chosen degree $r$ polynomial, and considering at each of these points a set of $s$ evenly distributed rotation matrices. This construction yields a new upper bound on the minimal logarithmic energy of $n=rs$ rotation matrices.

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Carlos Beltrán, Federico Carrasco, Damir Ferizović, Pedro R. López-Gómez. 2025-06-16. Points on $\operatorname{SO}(3)$ with low logarithmic energy. https://arxiv.org/abs/2506.13388

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