Let i. i. d. symmetric Bernoulli random variables be associated to the edges of a binary tree having n levels. With any leaf of the tree we associate the sum of variables along the path connecting the leaf with the tree root. Let M n denote the maximum of all such sums. We prove that, as n grows, the distributions of M n approach some helix in the space of distributions. Each element of this helix is an accumulation point for shifts of distributions of M n . Bibliography 13 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 408, 2012, pp. 268–284.
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Lifshits, M.A. Cyclic Behavior of Maxima in a Hierarchical Summation Scheme. J Math Sci 199, 215–224 (2014). https://doi.org/10.1007/s10958-014-1848-5
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DOI: https://doi.org/10.1007/s10958-014-1848-5