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}
}
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. 

Figures from this paper

Continuum and thermodynamic limits for a simple random-exchange model

References

SHOWING 1-10 OF 30 REFERENCES
Mixing times for random k-cycles and coalescence-fragmentation chains
Kac's Walk on $n$-sphere mixes in $n\log n$ steps
Emergence of Giant Cycles and Slowdown Transition in Random Transpositions and k-Cycles
Compositions of Random Transpositions
A lecture on the averaging process
A Gibbs sampler on the $n$-simplex
...
1
2
3
...