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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
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2242879
Page Count: 9
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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.
The Annals of Probability © 1979 Institute of Mathematical Statistics