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A PHASE TRANSITION FOR REPEATED AVERAGES
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Journal Article
A PHASE TRANSITION FOR REPEATED AVERAGES
2022
Overview
Let x₁, . . . , xn
be a fixed sequence of real numbers. At each stage, pick two indices I and J uniformly at random, and replace xI, xJ
by (xI
+ xJ
)/2, (xI
+ xJ
)/2. Clearly, all the coordinates converge to (x₁ +···+ xn
)/n. We determine the rate of convergence, establishing a sharp “cutoff” transition answering a question of Jean Bourgain.
Publisher
Institute of Mathematical Statistics
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