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Teoriya Veroyatnostei i ee Primeneniya, 1996, Volume 41, Issue 2, Pages 272–283
DOI: https://doi.org/10.4213/tvp2932 (Mi tvp2932) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Limit theorems for a random covering of a finite setand for the number of solutions of a system of random equations

V. G. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (620 kB) Citations (9)
DOI: https://doi.org/10.4213/tvp2932
Abstract: The paper deals with the problem of covering a finite set by its random subsets selected at random and independently. The probability laws of the selection of the random sets are allowed to vary from trial to trial which is essentially new for the problem under consideration. The principal result is a Poisson limit theorem for the number of uncovered points. This theorem is illustrated by two schemes of group allocation of particles and is used to show that the number of solutions of a consistent random equation system with respect to the binary vector of unknowns has asymptotically logarithmic Poisson distribution.
Keywords: group allocation of particles, the number of empty cells, Poisson limit theorem, random equation systems.
Received: 20.04.1993
English version:
Theory of Probability and its Applications, 1997, Volume 41, Issue 2, Pages 265–274
DOI: https://doi.org/10.1137/S0040585X97975472
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. G. Mikhailov, “Limit theorems for a random covering of a finite setand for the number of solutions of a system of random equations”, Teor. Veroyatnost. i Primenen., 41:2 (1996), 272–283; Theory Probab. Appl., 41:2 (1997), 265–274
Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 1997
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\issue 2
\pages 265--274
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  • https://www.mathnet.ru/eng/tvp/v41/i2/p272
    • This publication is cited in the following 9 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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