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On the number of ones in outcome sequence of extended Pohl generator

Authors
  • Mezhennaya, Natalia M.1
  • Mikhailov, Vladimir G.2
  • 1 Bauman Moscow State Technical University, Russia , (Russia)
  • 2 Steklov Mathematical Institute of Russian Academy of Sciences, Russia , (Russia)
Type
Published Article
Journal
Discrete Mathematics and Applications
Publisher
De Gruyter
Publication Date
Oct 17, 2020
Volume
30
Issue
5
Pages
327–337
Identifiers
DOI: 10.1515/dma-2020-0029
Source
De Gruyter
Keywords
License
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Abstract

Formulas for distributions of number of ones (non-zeroes) in the cycle of the output sequence of generalized binary Pohl generator are obtained. Limit theorems for these distributions are derived in the case when the lengths of registers are coprime and tend to infinity, the contents of different registers are independent, but cell contents within each register may be dependent. The consequences of these theorems are given for the case when the contents of cells are independent random variables having equiprobable distribution on {0, 1}.

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