The minimal spherical dispersion

03/22/2021

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by   Simon Breneis, et al.

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In this paper we prove upper and lower bounds on the minimal spherical dispersion. In particular, we see that the inverse N(ε,d) of the minimal spherical dispersion is, for fixed ε>0, up to logarithmic terms linear in the dimension d. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere.