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arXiv · 1102.2556

Orbit equivalence and sofic approximation

Ken Dykema·David Kerr·Mikael Pichot
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Abstract

Given an ergodic probability measure preserving dynamical system $\G\acts (X,μ)$, where $\G$ is a finitely generated countable group, we show that the asymptotic growth of the number of finite models for the dynamics, in the sense of sofic approximations, is an invariant of orbit equivalence. We then prove an additivity formula for free products with amenable (possibly trivial) amalgamation. In particular, we obtain purely combinatorial proofs of several results in orbit equivalence theory.

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Ken Dykema, David Kerr, Mikael Pichot. 2011-12-20. Orbit equivalence and sofic approximation. https://arxiv.org/abs/1102.2556

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