Spherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant

Johann S. Brauchart, Josef Dick, Friedrich Pillichshammer

We prove that the information complexity (i.e., the inverse) of the classical spherical cap $L_2$ discrepancy on the $d$-dimensional sphere ${\mathbb{S}}^d$ decreases with dimension…