TY - JOUR A1 - Prochno, Joscha A1 - Rudolf, Daniel T1 - The minimal spherical dispersion JF - The Journal of Geometric Analysis N2 - We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy in (Anz Österreich Akad Wiss Math Nat Kl 132:3–10, 1995). In particular, we see that the inverse N(ε,d)of the minimal spherical dispersion is, for fixed ε>0, linear in the dimension d of the ambient space. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere. In terms of the corresponding inverse N~(ε,d), our bounds are optimal with respect to the dependence on ε. KW - Dispersion KW - Expected dispersion KW - Spherical cap KW - Spherical dispersion KW - VC-dimension Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2405020842543.936733306281 SN - 1050-6926 SN - 1559-002X VL - 34 IS - 3 PB - Springer US CY - New York ER -