Article
Average Distance Between Consecutive Points of Uniformly Distributed Sequences
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Abstract
In this paper we give best possible lower and upper bounds on the average distance between consecutive points of uniformly distributed sequences. The upper bound is attained with the dyadic van der Corput sequence. Further- more we give a constructive proof that any element from the interval [0, 1/2] can be obtained as the average distance between consecutive points of some uniformly distributed sequence.
Keywords
Uniform distribution, van der Corput sequence, (nα)-sequence.F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of.
Citation
Pillichshammer, F. & Steinerberger, S. (2009). Average distance between consecutive points of uniformly distributed sequences. Uniform Distribution Theory, 4(1), 51–67.
F. Pillichshammer and S. Steinerberger, “Average distance between consecutive points of uniformly distributed sequences,” Uniform Distribution Theory, vol. 4, no. 1, pp. 51–67, 2009.
Pillichshammer F, Steinerberger S. Average distance between consecutive points of uniformly distributed sequences. Uniform Distribution Theory. 2009;4(1):51–67.
Pillichshammer, F. and Steinerberger, S. (2009), ‘Average distance between consecutive points of uniformly distributed sequences’, Uniform Distribution Theory, 4(1), pp. 51–67.
Pillichshammer, Friedrich, and Stefan Steinerberger. “Average Distance Between Consecutive Points of Uniformly Distributed Sequences.” Uniform Distribution Theory, vol. 4, no. 1, 2009, pp. 51–67.
Pillichshammer, Friedrich, and Stefan Steinerberger. “Average Distance Between Consecutive Points of Uniformly Distributed Sequences.” Uniform Distribution Theory 4, no. 1 (2009): 51–67.
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Published by: Engineering Journals
