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Mat. Vopr. Kriptogr., 2012, Volume 3, Issue 3, Pages 35–55 (Mi mvk60)  

This article is cited in 2 scientific papers (total in 2 papers)

Conditions of convergence to the Poisson distribution for the number of solutions of random inclusions

V. A. Kopytceva, V. G. Mikhailovb

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

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; let $D\subset V^n$, $B\subset V^T$. For the number of solutions of random inclusions $x\in D$, $F(x)\in B$ we find new sufficient conditions of weak convergence to the Poisson law as $n,T\to\infty$.

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

DOI: https://doi.org/10.4213/mvk60

Full text: PDF file (178 kB)
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UDC: 519.212.2+519.214.5
Received 20.V.2011

Citation: V. A. Kopytcev, V. G. Mikhailov, “Conditions of convergence to the Poisson distribution for the number of solutions of random inclusions”, Mat. Vopr. Kriptogr., 3:3 (2012), 35–55

Citation in format AMSBIB
\Bibitem{KopMik12}
\by V.~A.~Kopytcev, V.~G.~Mikhailov
\paper Conditions of convergence to the Poisson distribution for the number of solutions of random inclusions
\jour Mat. Vopr. Kriptogr.
\yr 2012
\vol 3
\issue 3
\pages 35--55
\mathnet{http://mi.mathnet.ru/mvk60}
\crossref{https://doi.org/10.4213/mvk60}


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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, “Ob odnom asimptoticheskom svoistve sfer v diskretnykh prostranstvakh bolshoi razmernosti”, Matem. vopr. kriptogr., 5:1 (2014), 73–83  mathnet  crossref
    2. 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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