A PHASE TRANSITION FOR REPEATED AVERAGES

• 成果类型: Article
• 署名作者: Chatterjee, Sourav; Diaconis, Persi; Sly, Allan; Zhang, Lingfu
• 署名单位: Stanford University; Stanford University; Princeton University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1526
• 发表日期: 2022
• 页码: 1-17
• 关键词: random-walks; consensus; cycles

摘要

Let x(1), ..., x(n) be a fixed sequence of real numbers. At each stage, pick two indices I and J uniformly at random, and replace x(I), x(J) by (x(I) +x(J))/2, (x(I) +x(J))/2. Clearly, all the coordinates converge to (x(1)+ ...+ x(n))/n. We determine the rate of convergence, establishing a sharp cutoff transition answering a question of Jean Bourgain.