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Expected dispersion of uniformly distributed points

by   Aicke Hinrichs, et al.
Johannes Kepler University Linz
The University of Göttingen

The dispersion of a point set in [0,1]^d is the volume of the largest axis parallel box inside the unit cube that does not intersect with the point set. We study the expected dispersion with respect to a random set of n points determined by an i.i.d. sequence of uniformly distributed random variables. Depending on the number of points n and the dimension d we provide an upper and lower bound of the expected dispersion. In particular, we show that the minimal number of points required to achieve an expected dispersion less than ε∈(0,1) depends linearly on the dimension d.


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