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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 4, Pages 791–797
DOI: https://doi.org/10.4213/tvp5312 (Mi tvp5312) 		 
Short Communications

A remark on the distribution of values for functions of a large number of variables

V. A. Zorich

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/tvp5312
Abstract: 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, normal distribution, measure concentration principle.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00592-а
Received: 11.04.2019
Accepted: 19.06.2019
English version:
Theory of Probability and its Applications, 2020, Volume 64, Issue 4, Pages 631–635
DOI: https://doi.org/10.1137/S0040585X97T98974X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Zorich, “A remark on the distribution of values for functions of a large number of variables”, Teor. Veroyatnost. i Primenen., 64:4 (2019), 791–797; Theory Probab. Appl., 64:4 (2020), 631–635
Citation in format AMSBIB
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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