Michael Gnewuch:

Bounds for the average L^p-extreme and the L^∞-extreme discrepancy

The extreme or unanchored discrepancy is the geometric discrepancy of point sets in the d-dimensional unit cube with respect to the set system of axis-parallel boxes. For all natural even numbers p we provide upper bounds for the average L^p-extreme discrepancy. With these bounds we are able to derive upper bounds for the inverse of the L^∞-extreme discrepancy with optimal dependence on the dimension d and explicitly given constants.

Mathematics Subject Classification (1991): 11K38

Bibliographical note: Electronic Journal of Combinatorics, Vol. 12(1), Research Paper 54, October 2005.

Keywords: extreme discrepancy, star-discrepancy

Mail an Jens Burmeister

[Thu Feb 19 18:56:36 2009]

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