Abstract
In one dimension, we represent the diaphony as the L2-norm of a random process which is found to converge weakly to a second order stationary Gaussian; up to scaling, this implies the asymptotic distributions of the diaphony and the *-discrepancy to coincide. Further, we show that properly normalized, the diaphony of n points in dimension d is asymptotically Gaussian if both n and d increase with a certain rate.
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Research supported by the Austrian Science Foundation (FWF), project no P11143-MAT.
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Leeb, H. (1998). Weak limits for the diaphony. In: Niederreiter, H., Hellekalek, P., Larcher, G., Zinterhof, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods 1996. Lecture Notes in Statistics, vol 127. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1690-2_23
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DOI: https://doi.org/10.1007/978-1-4612-1690-2_23
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