Hammersley's Law for the van der Corput Sequence. An Instance of Probability Theory for Pseudo-Random Numbers

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 09, 1978
Accession Number
ADA061377

Entities

People

  • A. Del Junco
  • J. M. Steele

Organizations

  • Stanford University

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DTIC Thesaurus Topics

  • Abstracts
  • Analogs
  • Binary Notation
  • Computer Simulations
  • Identities
  • Inequalities
  • Military Research
  • Numbers
  • Numerical Integration
  • Probability
  • Pseudo Random Sequences
  • Random Variables
  • Security
  • Sequences
  • Statistics
  • United States
  • United States Government

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  • Computer Programming and Software Development.
  • Mathematical Modeling and Probability Theory.