Orbit equivalence and sofic approximation

2011/02/13 by Ken Dykema, David Kerr, Dykema, Ken +3 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1102.2556

openalex publication_date 2011/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On Groups of Measure Preserving Transformations. I
• Limit laws for Random matrices and free products

Cited by

• Sofic dimension for discrete measured groupoids
• Universal entropy invariants

Related

• Applications of orbit equivalence to actions of discrete amenable groups
• Behaviour of entropy under bounded and integrable orbit equivalence
• Approximate equivalence of actions
• An Uncountable Family of Non Orbit Equivalent Actions of \Bbb F_n
• Orbit Equivalence and Measured Group Theory