Article
An Exact Formula for the L Discrepancy 2 of the Shifted Hammersley Point Set
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Abstract
In this note we prove an exact formula for the L2 discrepancy of the shifted two-dimensional Hammersley point set in base 2. Our formula shows that this quantity only depends on the number of zero digits in the dyadic expansion of the shift and the cardinality of the point set. Our result is the solution to an open problem stated by O. Strauch. Further we obtain the best shifts from our formula and we show that the L2 discrepancy of the shifted two- dimensional Hammersley point set in base 2 satisfies a central limit theorem.
Keywords
L2 discrepancy, Hammersley point set, digital shift.
Citation
Kritzer, P. & Pillichshammer, F. (2006). An exact formula for the l discrepancy 2 of the shifted hammersley point set. Uniform Distribution Theory, 1(1), 1–13.
P. Kritzer and F. Pillichshammer, “An exact formula for the l discrepancy 2 of the shifted hammersley point set,” Uniform Distribution Theory, vol. 1, no. 1, pp. 1–13, 2006.
Kritzer P, Pillichshammer F. An exact formula for the l discrepancy 2 of the shifted hammersley point set. Uniform Distribution Theory. 2006;1(1):1–13.
Kritzer, P. and Pillichshammer, F. (2006), ‘An exact formula for the l discrepancy 2 of the shifted hammersley point set’, Uniform Distribution Theory, 1(1), pp. 1–13.
Kritzer, Peter, and Friedrich Pillichshammer. “An Exact Formula for the L Discrepancy 2 of the Shifted Hammersley Point Set.” Uniform Distribution Theory, vol. 1, no. 1, 2006, pp. 1–13.
Kritzer, Peter, and Friedrich Pillichshammer. “An Exact Formula for the L Discrepancy 2 of the Shifted Hammersley Point Set.” Uniform Distribution Theory 1, no. 1 (2006): 1–13.
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Published by: Engineering Journals
