The ergodic theory of free group actions: entropy and the \(f\)-invariant

DOI10.4171/GGD/89zbMath1201.37006arXiv0902.0174MaRDI QIDQ990727

Lewis Phylip Bowen

Publication date: 1 September 2010

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.0174

zbMATH Keywords

entropyfree groupmeasure-conjugacy invariant

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35)

Related Items (23)

Fuglede-Kadison determinants and sofic entropy ⋮ Finite entropy actions of free groups, rigidity of stabilizers, and a Howe-Moore type phenomenon ⋮ An asymptotic equipartition property for measures on model spaces ⋮ Announce of an entropy formula for a class of actions coming from Gibbs measures ⋮ The relative f-invariant and non-uniform random sofic approximations ⋮ On the almost eigenvectors of random regular graphs ⋮ Correlation Bounds for Distant Parts of Factor of IID Processes ⋮ Spectral measures of factor of i.i.d. processes on vertex-transitive graphs ⋮ ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES ⋮ Bernoulli actions of sofic groups have completely positive entropy ⋮ Mean dimensions for partial actions ⋮ A subgroup formula for f-invariant entropy ⋮ Residually finite actions and crossed products ⋮ Entropy theory for sofic groupoids. I: The foundations ⋮ Measure conjugacy invariants for actions of countable sofic groups ⋮ Entropy and expansion ⋮ The work of Lewis Bowen on the entropy theory of non-amenable group actions ⋮ Ergodic actions of countable groups and finite generating partitions ⋮ Examples in the entropy theory of countable group actions ⋮ Mutual information decay for factors of i.i.d. ⋮ Entropy inequalities for factors of IID ⋮ Sofic homological invariants and the Weak Pinsker Property ⋮ Entropy for partial actions of ℤ

Cites Work

• A measure-conjugacy invariant for free group actions
• On isomorphism of weak Bernoulli transformations
• Factors of Bernoulli shifts are Bernoulli shifts
• Non-abelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula
• On the cohomology of Bernoulli actions
• Measure conjugacy invariants for actions of countable sofic groups

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