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Mat. Vopr. Kriptogr., 2010, Volume 1, Issue 4, Pages 63–84 (Mi mvk21)  

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

Poisson type theorems for the number of solutions of random inclusions

V. A. Kopyttsevab, V. G. Mikhailovab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Academy of Cryptography of Russian Federation

Abstract: Let $F$ be a random mapping of $n$-dimensional space $V^n$ over the finite field $GF(q)$ into $T$-dimensional space $V^T$ over the same field, and $D\subset V^n$, $B\subset V^T$. For systems of inclusions $x\in D$, $F(x)\in B$ sufficient conditions for the weak convergence of the number of solutions to the Poisson type laws as $n,T\to\infty$ are obtained.

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

DOI: https://doi.org/10.4213/mvk21

Full text: PDF file (184 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.212.2
Received 20.IV.2010

Citation: V. A. Kopyttsev, V. G. Mikhailov, “Poisson type theorems for the number of solutions of random inclusions”, Mat. Vopr. Kriptogr., 1:4 (2010), 63–84

Citation in format AMSBIB
\Bibitem{KopMik10}
\by V.~A.~Kopyttsev, V.~G.~Mikhailov
\paper Poisson type theorems for the number of solutions of random inclusions
\jour Mat. Vopr. Kriptogr.
\yr 2010
\vol 1
\issue 4
\pages 63--84
\mathnet{http://mi.mathnet.ru/mvk21}
\crossref{https://doi.org/10.4213/mvk21}


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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, “O raspredelenii chisel reshenii sluchainykh vklyuchenii”, Matem. vopr. kriptogr., 2:2 (2011), 55–80  mathnet  crossref
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    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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