Soficity, amenability, and dynamical entropy
By David Kerr, Hanfeng Li. 2010
94 citations recorded by the source corpus.
In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen's sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical counterparts when the acting group is amenable.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3dbc898ad3c7568236047ff6a7f64cf4b35c7154
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In Geometry and Topology
- Ben Hayes
- David Kerr
- Hanfeng Li
- Valerio Capraro
- Martino Lupini
- Xiangdong Ye
- Eli Glasner
- Frederic Pierre Jean Latrémolière
In Mathematical Physics
Citations in the corpus
- Fuglede–Kadison Determinants and Sofic Entropy (2014, background): “4 in [22] this does not depend on the choice of dynamically generating pseudometric.”
- Entropy and the variational principle for actions of sofic groups (2010, unknown): “D S] 2 8 Fe b 20”
- Combinatorial Independence and Sofic Entropy (2012, methodology): “IE(X) is a closed G-invariant normal subgroup of X.”
- Sofic measure entropy via finite partitions (2011, background): “[5], [6]) and is automatic ifG is infinite.”
- 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.”
- Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, methodology): “It is shown in Section 5 of [76] using the so called Rokhlin lemma for sofic approximations of countable amenable groups (see Section 4 of [76]) that the sofic entropy associated with any sofic approximation sequence of an amenable group coincide with the classical notion of entropy for actions of a”