Classical spherical cap L2 discrepancy improves with dimension while a balanced large-cap variant yields polynomially growing integration errors in H^{(d+1)/2}(S^d) via Stolarsky invariance.
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Spherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant
Classical spherical cap L2 discrepancy improves with dimension while a balanced large-cap variant yields polynomially growing integration errors in H^{(d+1)/2}(S^d) via Stolarsky invariance.