Article
On the Limit Distribution of Consecutive Elements of the Van Der Corput Sequence
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Abstract
Recently, Fialov´a and Strauch, Uniform Distribution Theory, 6(1):101-125, 2011, calculated the asymptotic distribution function (adf) of the two-dimensional sequence (φ b(n), φ b(n + 1))n≥0, where (φ b(n))n≥0 denotes the van der Corput sequence in base b. In the present paper we solve the general problem asking for the limit distribution of (φ b(n), φ b(n+1), . . . , φ b(n+s−1))n≥0. We use the fact that the van der Corput sequence can be seen as the orbit of the origin under the ergodic von Neumann-Kakutani transformation.
Keywords
van der Corput sequence, von Neumann-Kakutani transformation, ergodic theory, low discrepancy sequences.
Citation
Aistleitner, C. & Hofer, M. (2013). On the limit distribution of consecutive elements of the van der corput sequence. Uniform Distribution Theory, 8(1), 89–96.
C. Aistleitner and M. Hofer, “On the limit distribution of consecutive elements of the van der corput sequence,” Uniform Distribution Theory, vol. 8, no. 1, pp. 89–96, 2013.
Aistleitner C, Hofer M. On the limit distribution of consecutive elements of the van der corput sequence. Uniform Distribution Theory. 2013;8(1):89–96.
Aistleitner, C. and Hofer, M. (2013), ‘On the limit distribution of consecutive elements of the van der corput sequence’, Uniform Distribution Theory, 8(1), pp. 89–96.
Aistleitner, Christoph, and Markus Hofer. “On the Limit Distribution of Consecutive Elements of the Van Der Corput Sequence.” Uniform Distribution Theory, vol. 8, no. 1, 2013, pp. 89–96.
Aistleitner, Christoph, and Markus Hofer. “On the Limit Distribution of Consecutive Elements of the Van Der Corput Sequence.” Uniform Distribution Theory 8, no. 1 (2013): 89–96.
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Published by: Engineering Journals
