# Invariant percolation and measured theory of nonamenable groups

@article{Houdayer2011InvariantPA, title={Invariant percolation and measured theory of nonamenable groups}, author={Cyril Houdayer}, journal={arXiv: Group Theory}, year={2011} }

Using percolation techniques, Gaboriau and Lyons recently proved that every countable, discrete, nonamenable group $\Gamma$ contains measurably the free group $\mathbf F_2$ on two generators: there exists a probability measure-preserving, essentially free, ergodic action of $\mathbf F_2$ on $([0, 1]^\Gamma, \lambda^\Gamma)$ such that almost every $\Gamma$-orbit of the Bernoulli shift splits into $\mathbf F_2$-orbits. A combination of this result and works of Ioana and Epstein shows that every…

## 18 Citations

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