不变性渗流与非顺从群的测度理论
Invariant percolation and measured theory of nonamenable groups
摘要：
利用渗流技术，加博里奥和里昂最近证明，每一个可数的，离散的，不服从组$Γ$包含可测量的自由群$\mathbf F_2$上的两个发电机：存在一个概率测度保持，基本上是免费的，遍历行动的$\mathbf F_2$对$([0, 1]^Γ, λ^Γ)$，使几乎每一个$Γ$ -轨道的伯努利转移分裂成$\mathbf F_2$ -轨道。这个结果和Ioana和Epstein的作品相结合表明，每个可数的，离散的，不服从的群允许不可数许多非轨道等价的作用。
英文摘要：
Using percolation techniques, Gaboriau and Lyons recently proved that every countable, discrete, nonamenable group $Γ$ 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 $([0, 1]^Γ, λ^Γ)$ such that almost every $Γ$-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 countable, discrete, nonamenable group admits uncountably many non-orbit equivalent actions.
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