Rigid actions have zero entropy
classification
🧮 math.DS
math.OA
keywords
entropyfreenonpositivesoficactionactionsessentiallyrigid
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Rigid actions have zero Rokhlin entropy and nonpositive sofic entropy. Because rigidity is a stable orbit-equivalence invariant, this provides the first example of an essentially free, ergodic, probability-measure-preserving action of the free group that has nonpositive sofic entropy and any essentially free action stably-orbit-equivalent to it also has nonpositive sofic entropy.
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