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Tr. Mat. Inst. Steklova, 2013, Volume 282, Pages 165–180 (Mi tm3497)  

This article is cited in 5 scientific papers (total in 5 papers)

Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications

V. G. Mikhailov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: The properties of the distribution of the number of empty cells are analyzed for a natural generalization of an equiprobable scheme for group allocation of particles. An error estimate is obtained for the Chen–Stein method of Poisson approximation for the distribution of the number of empty cells in this scheme. This estimate is used to derive sufficient conditions for the distribution of the number of empty cells to converge to the convolutions of the Poisson distribution and two-point distributions. On the basis of these results, asymptotic properties of the solution set of a perturbed system of linear Boolean equations are studied (in the case of consistent increase in the number of unknowns and the number of equations).

DOI: https://doi.org/10.1134/S037196851303014X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 282, 157–171

Bibliographic databases:

Document Type: Article
UDC: 519.212.2
Received in December 2012

Citation: V. G. Mikhailov, “Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 165–180; Proc. Steklov Inst. Math., 282 (2013), 157–171

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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. A. V. Volgin, “Asimptoticheskie svoistva mnozhestva reshenii iskazhennykh sistem uravnenii”, PDM. Prilozhenie, 2014, no. 7, 48–49  mathnet
    2. V. P. Chistyakov, “On the asymptotic normality of the number of empty cells in a scheme of group allocation of particles”, Discrete Math. Appl., 24:6 (2014), 319–325  mathnet  crossref  crossref  mathscinet  elib  elib
    3. V. P. Chistyakov, “Ob asimptoticheskoi normalnosti chisla pustykh yacheek v odnoi skheme razmescheniya chastits komplektami”, Matem. vopr. kriptogr., 5:4 (2014), 129–138  mathnet  crossref
    4. Galinina O., Turlikov A., Pyattaev A., Johnsson K., Andreev S., Koucheryavy Y., “a Capacity Bound For Mmwave-Based Channel Access in Ultra-Dense Wearable Deployments”, 2015 7Th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (Icumt), International Conference on Ultra Modern Telecommunications and Control Systems & Workshops, IEEE, 2015, 298–304  isi
    5. Galinina O., Pyattaev A., Johnsson K., Turlikov A., Andreev S., Koucheryavy Y., “Assessing System-Level Energy Efficiency of mmWave-Based Wearable Networks”, IEEE J. Sel. Areas Commun., 34:4 (2016), 923–937  crossref  isi  elib  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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