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 
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/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] M. Bramson, “Minimal displacement of branching random walk”, Z. Wahrsch. verw. Gebiete, 45 (1978), 89–108 | DOI | MR | Zbl

[2] M. A. Lifshits, “Tsiklicheskoe povedenie maksimuma summ nezavisimykh velichin”, Zap. nauchn. semin. POMI, 408, 2012, 268–284 | MR

[3] V. V. Petrov, “O veroyatnostyakh bolshikh uklonenii summ nezavisimykh sluchainykh velichin”, Teor. veroyatn. i eë primen., 10:2 (1965), 310–322 | MR | Zbl

[4] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR