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

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:

UDC: 519.212.2

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, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 165–180; Proc. Steklov Inst. Math., 282 (2013), 157–171

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3497
• https://doi.org/10.1134/S037196851303014X
• http://mi.mathnet.ru/eng/tm/v282/p165

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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
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
3. V. P. Chistyakov, “Ob asimptoticheskoi normalnosti chisla pustykh yacheek v odnoi skheme razmescheniya chastits komplektami”, Matem. vopr. kriptogr., 5:4 (2014), 129–138
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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
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