Sofic entropy and amenable groups

By Lewis Bowen. Ergodic Theory and Dynamical Systems, 2010

71 citations recorded by the source corpus.

Abstract In previous work, the author introduced a measure-conjugacy invariant for sofic group actions called sofic entropy. Here, it is proven that the sofic entropy of an amenable group action equals its classical entropy. The proof uses a new measure-conjugacy invariant called upper-sofic entropy and a theorem of Rudolph and Weiss for the entropy of orbit-equivalent actions relative to the orbit change σ-algebra.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/596982e951ab6d33f65573a045a6f91fab7ca4db

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In Algebra and Number Theory

1. David Kerr
2. Hanfeng Li
3. Frederic Pierre Jean Latrémolière
4. A. Kavruk

In Mathematical Physics

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In Statistical and Nonlinear Physics

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2. Hanfeng Li

Citations in the corpus

• Entropy and the variational principle for actions of sofic groups (2010, unknown): “In [3] Bowen showed that, when the acting group is amenable and there exists a generating finite measurable partition, the sofic measure entropy as defined in [5] is equal to the classical Kolmogorov-Sinai measure entropy, independently of the sofic approximation sequence.”
• Compact Group Automorphisms, Addition Formulas and Fuglede-Kadison Determinants (2010, background): “Compared to the positive case in step one, the main difficulty here is that the compression of f to a nonempty finite subset of Γ map fail to be invertible.”
• Soficity, amenability, and dynamical entropy (2010, methodology): “However, in the case that the acting group is amenable and there exists a generating finite partition, Bowen showed in [3] that sofic measure entropy coincides with classical Kolmogorov-Sinai entropy for all choices of sofic approximation sequence.”
• Sofic measure entropy via finite partitions (2011, background): “Recently Lewis Bowen greatly extended the scope of this classical theory to measure-preserving actions of countable sofic groups by replacing the internal information-theoretic approach of Kolmogorov with the statistical-mechanical idea of counting external finite models [1, 3].”