This article is cited in 2 papers

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

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.

Received: 11.04.2019
Accepted: 19.06.2019

DOI: 10.4213/tvp5312

 English version: Theory of Probability and its Applications, 2020, 64:4, 631–635

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