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Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers

A. del Junco and J. Michael Steele
The Annals of Probability
Vol. 7, No. 2 (Apr., 1979), pp. 267-275
Stable URL: http://www.jstor.org/stable/2242879
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers
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Abstract

The analogue of Hammersley's theorem on the length of the longest monotonic subsequence of independent, identically, and continuously distributed random variables is obtained for the pseudorandom van der Corput sequence. In this case there is no limit but the precise limits superior and inferior are determined. The constants obtained are closely related to those established in the independent case by Logan and Shepp, and Vershik and Kerov.

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