RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (178 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.2

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} 

• http://mi.mathnet.ru/eng/dm1032
• https://doi.org/10.4213/dm1032
• http://mi.mathnet.ru/eng/dm/v20/i4/p120

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
•  Number of views: This page: 258 Full text: 97 References: 31 First page: 17