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Diskr. Mat., 2003, Volume 15, Issue 2, Pages 128–137 (Mi dm200)  

This article is cited in 7 scientific papers (total in 7 papers)

Limit theorems for the number of points of a given set covered by a random linear subspace

V. G. Mikhailov


Abstract: Let $V^T$ be the $T$-dimensional linear space over a finite field $K$, and let $B_1,\ldots,B_m$ be subsets of $V^T$ not containing the zero-point. Let a subspace $L$ be chosen randomly and equiprobably from the set of all $n$-dimensional linear subspaces of $V^T$. We consider the number $\mu(B_i)$ of points in the intersections $L\cap B_i$, $i=1,\ldots,m$. We study the limit behaviour of the distribution of the vector $(\mu(B_1),\ldots,\mu(B_m))$ as $T,n\to \infty$ and the sets vary in such a way that the means of $\mu(B_i)$ tend to finite limits. The field $K$ is fixed. We prove that this random vector has in limit the compound Poisson distribution. Necessary and sufficient conditions for asymptotic independency of the random variables $\mu(B_1),\ldots,\mu(B_m)$ are derived.
This research was supported by the Russian Foundation for Basic Research, grants 02–01–00266 and 00–15–96136.

DOI: https://doi.org/10.4213/dm200

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English version:
Discrete Mathematics and Applications, 2003, 13:2, 179–188

Bibliographic databases:

Document Type: Article
UDC: 519.2
Received: 08.01.2003

Citation: V. G. Mikhailov, “Limit theorems for the number of points of a given set covered by a random linear subspace”, Diskr. Mat., 15:2 (2003), 128–137; Discrete Math. Appl., 13:2 (2003), 179–188

Citation in format AMSBIB
\Bibitem{Mik03}
\by V.~G.~Mikhailov
\paper Limit theorems for the number of points of a given set covered by a random linear subspace
\jour Diskr. Mat.
\yr 2003
\vol 15
\issue 2
\pages 128--137
\mathnet{http://mi.mathnet.ru/dm200}
\crossref{https://doi.org/10.4213/dm200}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2006682}
\zmath{https://zbmath.org/?q=an:1046.60010}
\transl
\jour Discrete Math. Appl.
\yr 2003
\vol 13
\issue 2
\pages 179--188
\crossref{https://doi.org/10.1515/156939203322109131}


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    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. G. Mikhailov, “Limit theorems for the number of solutions of a system of random linear equations belonging to a given set”, Discrete Math. Appl., 17:1 (2007), 13–22  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. V. A. Kopyttsev, V. G. Mikhailov, “Poisson-type theorems for the number of special solutions of a random linear inclusion”, Discrete Math. Appl., 20:2 (2010), 191–211  mathnet  crossref  crossref  mathscinet  elib
    3. V. A. Kopyttsev, V. G. Mikhailov, “Poisson-type limit theorems for the generalised linear inclusion”, Discrete Math. Appl., 22:4 (2012), 477–491  mathnet  crossref  crossref  mathscinet  elib  elib
    4. A. M. Zubkov, V. I. Kruglov, “Momentnye kharakteristiki vesov vektorov v sluchainykh dvoichnykh lineinykh kodakh”, Matem. vopr. kriptogr., 3:4 (2012), 55–70  mathnet  crossref
    5. A. M. Zubkov, V. I. Kruglov, “Statisticheskie kharakteristiki vesovykh spektrov sluchainykh lineinykh kodov nad $\mathrm{GF}(p)$”, Matem. vopr. kriptogr., 5:1 (2014), 27–38  mathnet  crossref
    6. V. A. Kopyttsev, V. G. Mikhailov, “Ob odnom asimptoticheskom svoistve sfer v diskretnykh prostranstvakh bolshoi razmernosti”, Matem. vopr. kriptogr., 5:1 (2014), 73–83  mathnet  crossref
    7. V. G. Mikhailov, “Formuly dlya odnoi kharakteristiki sfer i sharov v dvoichnykh prostranstvakh bolshoi razmernosti”, Diskret. matem., 30:2 (2018), 62–72  mathnet  crossref  elib
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