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Gaussian limits for discrepancies. I: Asymptotic results

Andre van Hameren·Ronald Kleiss·Jiri Hoogland
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Abstract

We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit $N\to\infty$. We then examine the circumstances under which this distribution approaches a normal distribution. For large classes of non-uniformity measures, a Law of Many Modes in the spirit of the Central Limit Theorem can be derived.

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Andre van Hameren, Ronald Kleiss, Jiri Hoogland. 1997-08-13. Gaussian limits for discrepancies. I: Asymptotic results. https://doi.org/10.1016/s0010-4655(97)00105-7

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