Geodesic
Cyclic behavior of maxima in a hierarchical summation scheme
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 268-284 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let i.i.d. symmetric Bernoulli random variables be associated to the edges of a binary tree having $n$ levels. To 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 the shifts of distributions of $M_n$. 
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M. A. Lifshits. Cyclic behavior of maxima in a hierarchical summation scheme. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 268-284. http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a15/

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