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Localized large sums of random variables. (English) Zbl 1133.60322

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.

MSC:

60G50 Sums of independent random variables; random walks
11N25 Distribution of integers with specified multiplicative constraints
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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
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