@article{3991dea361a447ef9340696af4e65c0d,
title = "A PHASE TRANSITION FOR REPEATED AVERAGES",
abstract = "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.",
keywords = "Convergence rate, Cutoff phenomenon, Markov chain",
author = "Sourav Chatterjee and Persi Diaconis and Allan Sly and Lingfu Zhang",
note = "Funding Information: Funding. Sourav Chatterjee{\textquoteright}s research was partially supported by NSF Grant DMS-1855484. Persi Diaconis{\textquoteright}s research was partially supported by NSF Grant DMS-0804324. Allan Sly{\textquoteright}s research was partially supported by NSF Grant DMS-1855527, Simons Investigator Grant and a MacArthur Fellowship. Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2022",
year = "2022",
month = jan,
doi = "10.1214/21-AOP1526",
language = "English (US)",
volume = "50",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "1",
}