Geodesic
A~remark on the distribution of values for functions of a large number of variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 4, pp. 791-797

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It is known that the values of functions that depend on a large number of similar variables are almost constant from the point of view of an observer evaluating their values at random points of the domains of their definition (the “nonlinear law of large numbers”). We show that, under certain normalization conditions, the distribution of values of such functions tends to a normal distribution as the number of variables grows.
Keywords: law of large numbers, measure concentration principle.
Mots-clés : normal distribution 
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     author = {V. A. Zorich},
     title = {A~remark on the distribution of values for functions of a large number of variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {791--797},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_4_a8/}
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V. A. Zorich. A~remark on the distribution of values for functions of a large number of variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 4, pp. 791-797. http://geodesic.mathdoc.fr/item/TVP_2019_64_4_a8/