Corpus ID: 207847431

# Note on repeated random averages

```@article{Chatterjee2019NoteOR,
title={Note on repeated random averages},
author={S. Chatterjee and P. Diaconis},
journal={arXiv: Probability},
year={2019}
}```
• Published 2019
• Mathematics
• arXiv: Probability
Let \$x_1,\ldots,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+\cdots+x_n)/n\$. We address the rate of convergence in various norms. This answers a question of Jean Bourgain.
1 Citations

#### References

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