Geodesic
Cyclic behavior of the maximum of sums of independent random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 207-214

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In a recent author's work the cyclic behavior of maxima in a hierarchical summation scheme was discovered. In the present note we show how the same phenomenon appears in the scheme of conventional summation: the distribution of maximum of $2^n$ independent copies of a sum of $n$ i.i.d. random variables approaches, as $n$ grows, some helix in the space of distributions. 
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     author = {M. A. Lifshits},
     title = {Cyclic behavior of the maximum of  sums of independent random variables},
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     pages = {207--214},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a9/}
}
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M. A. Lifshits. Cyclic behavior of the maximum of  sums of independent random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 207-214. http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a9/