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

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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 $M_n$. 
@article{ZNSL_2012_408_a15,
     author = {M. A. Lifshits},
     title = {Cyclic behavior of maxima  in a~hierarchical summation scheme},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {268--284},
     publisher = {mathdoc},
     volume = {408},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a15/}
}
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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/