Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers
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Physical Sciences and Mathematics
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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.
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1979
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The Annals of Probability
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At the time of publication, author J. Michael Steele was affiliated with Stanford University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.