@article{ProchnoRudolf2024, author = {Prochno, Joscha and Rudolf, Daniel}, title = {The minimal spherical dispersion}, series = {The Journal of Geometric Analysis}, volume = {34}, journal = {The Journal of Geometric Analysis}, number = {3}, publisher = {Springer US}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-023-01527-z}, url = {http://nbn-resolving.de/urn:nbn:de:101:1-2405020842543.936733306281}, pages = {14 Seiten}, year = {2024}, abstract = {We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy in (Anz {\"O}sterreich 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.}, language = {en} }