Cyclic behavior of maxima in a hierarchical summation scheme
| Autor: | Lifshits, M. A. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | J.Math.Sci., 2014, 199, 2, 215-224 (English) Zapiski Nauchn.Semin POMI,2012,408,268-284 (Russian) |
| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
| Externí odkaz: |
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