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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 3, Pages 598–606
DOI: https://doi.org/10.4213/tvp1564 (Mi tvp1564) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

Limit theorems for the number of nonzero solutions of a system of random equations over GF(2)

V. G. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (470 kB) Citations (6)
DOI: https://doi.org/10.4213/tvp1564
Abstract: The asymptotic behavior of a number of solutions of a system of random equations of a particular form over GF(2) is investigated. The left-hand sides of the equations of the system are products of independent equiprobable linear functions in $n$ variables for GF(2), whereas the right-hand sides are equal to zero. Under the natural restrictions on the way of changing the parameters of the scheme (the number of unknowns, the number of equations, and the number of multipliers in the left-hand side of each equation) it is shown that the distribution of the number of nonzero solutions converges to a Poisson distribution. Sufficient conditions are given for the number of nonzero solutions to be asymptotically normal. The proofs are based on the moment method.
Keywords: systems of random equations, number of solutions, Poisson distribution.
Received: 03.12.1997
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 3, Pages 480–487
DOI: https://doi.org/10.1137/S0040585X97977082
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. G. Mikhailov, “Limit theorems for the number of nonzero solutions of a system of random equations over GF(2)”, Teor. Veroyatnost. i Primenen., 43:3 (1998), 598–606; Theory Probab. Appl., 43:3 (1999), 480–487
Citation in format AMSBIB
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\pages 598--606
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\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 3
\pages 480--487
\crossref{https://doi.org/10.1137/S0040585X97977082}
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  • https://www.mathnet.ru/eng/tvp1564
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  • https://www.mathnet.ru/eng/tvp/v43/i3/p598
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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