The minimal spherical dispersion

In this paper we prove upper and lower bounds on the minimal spherical dispersion. In particular, we see that the inverse $N(varepsilon,d)$ of the minimal spherical dispersion is, for fixed $varepsilon>0$, 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.