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: The analogue of Hammersley's theorem on the length of the longest monotonic subsequence of i.i.d. continously distributed random variables is obtained for the pseudo-random van der Corput sequence. In this case there is no limit but the precise liminf and limsup are determined. The constants obtained are closely related to those established in the independent case by Logan and Shepp, and Vershik and Kerov.

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