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April, 1979 Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers
A. del Junco, J. Michael Steele
Ann. Probab. 7(2): 267-275 (April, 1979). DOI: 10.1214/aop/1176995087

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.

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A. del Junco. J. Michael Steele. "Hammersley's Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers." Ann. Probab. 7 (2) 267 - 275, April, 1979. https://doi.org/10.1214/aop/1176995087

Information

Published: April, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0398.60011
MathSciNet: MR525053
Digital Object Identifier: 10.1214/aop/1176995087

Subjects:
Primary: 60C05
Secondary: 65C10

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 2 • April, 1979
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