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Mat. Vopr. Kriptogr., 2011, Volume 2, Issue 2, Pages 55–80 (Mi mvk31)  

This article is cited in 6 scientific papers (total in 6 papers)

On the distribution of the numbers of solutions of random inclusions

V. A. Kopytceva, V. G. Mikhailovb

a Academy of Cryptography of Russian Federation, Moscow
b Steklov Mathematical Institute of RAS, Moscow

Abstract: For given sets $D$ and $B$ of vectors in linear spaces $V^n$ and $V^T$ over the field $K=GF(q)$ we consider the number of solutions $\xi(D,F,B)$ of the system of inclusions $x\in D$, $A_1x+A_2 f(x)\in B$, where $A_1$ and $A_2$ are random $T\times n$ and $T\times m$ matrices over $K$ with independent elements and $f\colon V^n\to V^m$ is a given mapping. Sufficient conditions for the convergence of distributions of $\xi(D,F,B)$ to the Poisson or compound Poisson distributions are found. Results are applied to the number of solutions of a system of random polynomial equations.

Key words: random inclusions, systems of random equations, number of solutions, Poisson limit theorem.

DOI: https://doi.org/10.4213/mvk31

Full text: PDF file (208 kB)
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Document Type: Article
UDC: 519.212.2
Received 25.I.2011

Citation: V. A. Kopytcev, V. G. Mikhailov, “On the distribution of the numbers of solutions of random inclusions”, Mat. Vopr. Kriptogr., 2:2 (2011), 55–80

Citation in format AMSBIB
\Bibitem{KopMik11}
\by V.~A.~Kopytcev, V.~G.~Mikhailov
\paper On the distribution of the numbers of solutions of random inclusions
\jour Mat. Vopr. Kriptogr.
\yr 2011
\vol 2
\issue 2
\pages 55--80
\mathnet{http://mi.mathnet.ru/mvk31}
\crossref{https://doi.org/10.4213/mvk31}


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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, “Poisson-type limit theorems for the generalised linear inclusion”, Discrete Math. Appl., 22:4 (2012), 477–491  mathnet  crossref  crossref  mathscinet  elib  elib
    2. V. A. Kopyttsev, V. G. Mikhailov, “Usloviya skhodimosti k raspredeleniyu Puassona dlya chisel reshenii sluchainykh vklyuchenii”, Matem. vopr. kriptogr., 3:3 (2012), 35–55  mathnet  crossref
    3. 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
    4. 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
    5. V. A. Kopyttsev, V. G. Mikhailov, “Yavnye otsenki tochnosti puassonovskoi approksimatsii dlya raspredeleniya chisla reshenii sluchainykh vklyuchenii”, Matem. vopr. kriptogr., 6:1 (2015), 57–79  mathnet  crossref  mathscinet  elib
    6. 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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