2008/06/03 by Adrian Ioana, Ioana, A., Alexander S. Kechris +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.0806.0430
openalex publication_date 2008/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent co-inducing construction of Epstein to produce new kinds of mixing actions of an arbitrary infinite discrete group and it is also used to show that orbit equivalence of free, measure preserving, mixing actions of non-amenable groups is unclassifiable in a strong sense. Finally, in the case of property (T) groups we discuss connections with invariant percolation on Cayley graphs and the calculation of costs.