Figueiredo, A. D.; Da Rocha Filho, T. M.; Amato, M. A. Distribution probability of force for a physical system of \(N\) random particles. (English) Zbl 1448.70028 J. Math. Phys. 60, No. 7, 073301, 21 p. (2019). Summary: The present paper attempts to address a discussion on mathematical grounds of a model to associate the generalized version of the central limit theorem and the \(N\)-body problem related to the calculation of the force on a single star or particle due to the \(N - 1\) stars or particles whenever they are randomly distributed in the space and \(N \rightarrow \infty\). We calculate the resultant force on a test particle immersed in an \(N\)-particle system under a \(1/r^{\delta}\) force (\(\delta>0\)) and discuss the limit force under different approaches referred to as the Vlasov limit and the fluctuation limit. Also, one shows the behavior of the limit force in different domains for the Lévy exponent (\(\alpha\)). ©2019 American Institute of Physics MSC: 70F10 \(n\)-body problems 60F05 Central limit and other weak theorems 60G52 Stable stochastic processes Keywords:\(N\) random particles PDFBibTeX XMLCite \textit{A. D. Figueiredo} et al., J. Math. Phys. 60, No. 7, 073301, 21 p. (2019; Zbl 1448.70028) Full Text: DOI arXiv References: [1] Lévy, P., Théorie des erreurs. La loi de Gauss et les lois exceptionalles, Bull. Soc. Math. France, 2, 49-85 (1924) · JFM 50.0653.01 [2] Lévy, P., Sur les lois stables em calcul des probabilités, C. R. Acad. Sci., 176, 1284-1286 (1923) · JFM 49.0365.02 [3] Lévy, P., Integrales à éléments aléatoires indépendants et lois stables á n variables, C. R. Acad. 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