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Published in Russian in Doklady Akademii Nauk, 2013, Vol. 451, No. 4, pp. 374–377.
The article was translated by the authors.
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Grabchak, M., Molchanov, S.A. Limit theorems and phase transitions for two models of summation of iid random variables depending on parameters. Dokl. Math. 88, 431–434 (2013). https://doi.org/10.1134/S1064562413030204