J. Brauchart

collaborators

2 papers

math.NA2026

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 $S^{d}$ decreases with dimension…

math.CA2025

On the lower bounds for the spherical cap discrepancy

Dmitriy Bilyk, Johann S. Brauchart

We start by providing a very simple and elementary new proof of the classical bound due to J. Beck which states that the spherical cap $L_{2}$ -discrepancy of any $N$ points…

Spherical Cap L2​ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant

On the lower bounds for the spherical cap discrepancy

Spherical Cap $L_{2}$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant