Asymptotics for Minimal Discrete Energy on the Sphere

@inproceedings{Kuijlaars1997AsymptoticsFM,
title={Asymptotics for Minimal Discrete Energy on the Sphere},
author={B. J. Kuijlaars},
year={1997}
}

B. J. Kuijlaars

Published 1997

We investigate the energy of arrangements of N points on the surface of the unit sphere Sd in Rd+1 that interact through a power law potential V = 1/rs, where s > 0 and r is Euclidean distance. With Ed(s,N) denoting the minimal energy for such N-point arrangements we obtain bounds (valid for all N) for Ed(s, N) in the cases when 0 < s < d and 2 ≤ d < s. For s = d, we determine the precise asymptotic behavior of Ed(d,N) as N → ∞. As a corollary, lower bounds are given for the separation of any… CONTINUE READING