Subequivalence relations and positive-definite functions
Copyright policy )Subequivalence relations and positive-definite functions
We study a positive-definite function associated with a countable, measure-preserving equivalence relation, which can be used to measure quantitatively the proximity of subequivalence relations. Combined with a co-inducing construction introduced by Epstein and earlier work of Ioana, this can be used to construct many mixing actions of countable groups and establish the non-classifiability, in a strong sense, of orbit equivalence of actions of non-amenable groups. We also discuss connections with percolation on Cayley graphs and the theory of costs.
- California Institute of Technology United States
- University of California, San Diego United States
- Sorbonne Université France
Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, Probability (math.PR), property (T), Mathematics - Logic, Dynamical Systems (math.DS), subequivalence relations, percolation, property (T), non-amenable groups, positive-definite functions, orbit equivalence, 510, co-induced action, percolation, classification, cost, FOS: Mathematics, Subequivalence relations, Mathematics - Dynamical Systems, Logic (math.LO), Descriptive set theory, Mathematics - Probability
Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, Probability (math.PR), property (T), Mathematics - Logic, Dynamical Systems (math.DS), subequivalence relations, percolation, property (T), non-amenable groups, positive-definite functions, orbit equivalence, 510, co-induced action, percolation, classification, cost, FOS: Mathematics, Subequivalence relations, Mathematics - Dynamical Systems, Logic (math.LO), Descriptive set theory, Mathematics - Probability
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