Gaussian limits for discrepancies. I: Asymptotic results

Details Gaussian limits for discrepancies. I: Asymptotic results Gaussian limits for discrepancies. I: Asymptotic results

1997-08-13

arxiv.org/abs/physics/9708014v1

Physics

Computational Physics

25 pages, Latex, uses fleqn.sty, a4wide.sty, amsmath.sty

Scientific paper

10.1016/S0010-4655(97)00105-7

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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