Rigid actions have zero entropy

2015/07/28 by Lewis Bowen, Bowen, Lewis
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1507.07981

Abstract

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.

Related

• Sofic entropy, after Lewis Bowen, David Kerr and Hanfeng Li
• Sofic entropy and amenable groups
• Naive entropy of dynamical systems
• Entropy for actions of free groups under bounded orbit-equivalence
• Finite entropy actions of free groups, rigidity of stabilizers, and a\n Howe-Moore type phenomenon