Statistics Papers

Document Type

Journal Article

Date of this Version

1979

Publication Source

The Annals of Probability

Volume

7

Issue

2

Start Page

267

Last Page

275

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.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aop/1176995087#abstract

Comments

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.

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Date Posted: 27 November 2017

This document has been peer reviewed.