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Diskr. Mat., 2008, Volume 20, Issue 4, Pages 120–135 (Mi dm1032)  

This article is cited in 1 scientific paper (total in 1 paper)

Limit distributions of the number of vectors satisfying a linear relation

V. I. Kruglov


Abstract: Let $X_1,…,X_T$ be independent random elements uniformly distributed on a finite Abelian group $G$. In this paper, we give conditions under which the number of ordered sets $(i_1,…,i_k)$ of pairwise distinct numbers in $\{1,…,T\}$ such that $a_1X_{i_1}+…+a_kX_{i_k}=0$ where $a_1,…,a_k$ are fixed integers has the Poisson limit distribution as $T\to\infty$ and the group $G$ varies with $T$. We give an example of a sequence of groups $G$ for which the limit distribution of the number of ordered sets is the compound Poisson distribution.

DOI: https://doi.org/10.4213/dm1032

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English version:
Discrete Mathematics and Applications, 2008, 18:5, 465–481

Bibliographic databases:

UDC: 519.2
Received: 26.12.2007

Citation: V. I. Kruglov, “Limit distributions of the number of vectors satisfying a linear relation”, Diskr. Mat., 20:4 (2008), 120–135; Discrete Math. Appl., 18:5 (2008), 465–481

Citation in format AMSBIB
\Bibitem{Kru08}
\by V.~I.~Kruglov
\paper Limit distributions of the number of vectors satisfying a~linear relation
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 4
\pages 120--135
\mathnet{http://mi.mathnet.ru/dm1032}
\crossref{https://doi.org/10.4213/dm1032}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500610}
\zmath{https://zbmath.org/?q=an:1179.60018}
\elib{http://elibrary.ru/item.asp?id=20730272}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 5
\pages 465--481
\crossref{https://doi.org/10.1515/DMA.2008.034}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57649155492}


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  • https://doi.org/10.4213/dm1032
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Kopyttsev, V. G. Mikhailov, “An estimate of the approximation accuracy in B. A. Sevastyanov's limit theorem and its application in the problem of random inclusions”, Discrete Math. Appl., 25:3 (2015), 149–156  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Дискретная математика
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