Ford, Kevin; Tenenbaum, Gérald Localized large sums of random variables. (English) Zbl 1133.60322 Stat. Probab. Lett. 78, No. 1, 84-89 (2008). Summary: We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers. Cited in 1 ReviewCited in 1 Document MSC: 60G50 Sums of independent random variables; random walks 11N25 Distribution of integers with specified multiplicative constraints Keywords:sums of random variables; prime divisors PDFBibTeX XMLCite \textit{K. Ford} and \textit{G. Tenenbaum}, Stat. Probab. Lett. 78, No. 1, 84--89 (2008; Zbl 1133.60322) Full Text: DOI arXiv References: [1] Elliott, P.D.T.A., 1979. Probabilistic Number Theory, vol. I. Springer, New York.; Elliott, P.D.T.A., 1979. Probabilistic Number Theory, vol. I. Springer, New York. · Zbl 0431.10029 [2] Oon, S.M., 2005. Construction des suites binaires pseudo-aléatoires. Thèse d’université, Nancy, Université Henri Poincaré-Nancy 1, UFR STMIA, pp. 110.; Oon, S.M., 2005. Construction des suites binaires pseudo-aléatoires. Thèse d’université, Nancy, Université Henri Poincaré-Nancy 1, UFR STMIA, pp. 110. [3] Philipp, W., 1986. Invariance principles for independent and weakly dependent random variables. In: Dependence in Probability and Statistics, Oberwolfach, 1985, Progr. Probab. Statist. 11, Birkhäuser Boston, Boston, MA, pp. 225-268.; Philipp, W., 1986. Invariance principles for independent and weakly dependent random variables. In: Dependence in Probability and Statistics, Oberwolfach, 1985, Progr. Probab. Statist. 11, Birkhäuser Boston, Boston, MA, pp. 225-268. [4] Tenenbaum, G., 1999. Crible d’Ératosthène et modèle de Kubilius. In: Győry, K., Iwaniec, H., Urbanowicz, J. (Eds.), Number Theory in Progress. In: Proceedings of the conference in honor of Andrzej Schinzel, Zakopane, Poland 1997, Walter de Gruyter, Berlin, New York, pp. 1099-1129.; Tenenbaum, G., 1999. Crible d’Ératosthène et modèle de Kubilius. In: Győry, K., Iwaniec, H., Urbanowicz, J. (Eds.), Number Theory in Progress. In: Proceedings of the conference in honor of Andrzej Schinzel, Zakopane, Poland 1997, Walter de Gruyter, Berlin, New York, pp. 1099-1129. · Zbl 0936.11052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.