A PHASE TRANSITION FOR REPEATED AVERAGES

Sourav Chatterjee, Persi Diaconis, Allan Sly, Lingfu Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish (US)
JournalAnnals of Probability
Volume50
Issue number1
DOIs
StatePublished - Jan 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Convergence rate
  • Cutoff phenomenon
  • Markov chain

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