On the uniform distribution modulo 1 of multidimensional LS-sequences

Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani’s interval splitting procedure. Under an appropriate choice of the parameters and , such sequences have low discrepancy, which means that they are natural candidates for Quasi...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2014-10, Vol.193 (5), p.1329-1344
Main Authors: Aistleitner, Christoph, Hofer, Markus, Ziegler, Volker
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Parameters
Sequences
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Summary:Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani’s interval splitting procedure. Under an appropriate choice of the parameters and , such sequences have low discrepancy, which means that they are natural candidates for Quasi-Monte Carlo integration. It is tempting to assume that LS-sequences can be combined coordinatewise to obtain a multidimensional low-discrepancy sequence. However, in the present paper, we prove that this is not always the case: if the parameters and of two one-dimensional low-discrepancy LS-sequences satisfy certain number-theoretic conditions, then their two-dimensional combination is not even dense in .
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-013-0331-0