The Annals of Probability

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

A. del Junco and J. Michael Steele

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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.

Article information

Source
Ann. Probab. Volume 7, Number 2 (1979), 267-275.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995087

Digital Object Identifier
doi:10.1214/aop/1176995087

Mathematical Reviews number (MathSciNet)
MR525053

Zentralblatt MATH identifier
0398.60011

JSTOR
links.jstor.org

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 65C10: Random number generation

Keywords
Van der Corput sequence monotonic subsequence

Citation

del Junco, A.; Steele, J. Michael. Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers. Ann. Probab. 7 (1979), no. 2, 267--275. doi:10.1214/aop/1176995087. https://projecteuclid.org/euclid.aop/1176995087


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