Date of this Version
The Annals of Probability
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 original and published work is available at: https://projecteuclid.org/euclid.aop/1176995087#abstract
Junco, A. d., & Steele, J. M. (1979). Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers. The Annals of Probability, 7 (2), 267-275. http://dx.doi.org/10.1214/aop/1176995087
Date Posted: 27 November 2017
This document has been peer reviewed.