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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Convergence rate
- Cutoff phenomenon
- Markov chain