A brief introduction to sofic entropy theory

Preprint English OPEN
Bowen, Lewis;
(2017)
  • Subject: Mathematics - Dynamical Systems
    arxiv: Mathematics::Dynamical Systems | Nonlinear Sciences::Chaotic Dynamics | Computer Science::Discrete Mathematics | Computer Science::Formal Languages and Automata Theory | Mathematics::Operator Algebras

Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.
  • References (55)
    55 references, page 1 of 6

    [Bow10b] Lewis Bowen. Measure conjugacy invariants for actions of countable sofic groups. J. Amer. Math. Soc., 23(1):217-245, 2010.

    [Bow10c] Lewis Bowen. Non-abelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula. Ergodic Theory Dynam. Systems, 30(6):1629-1663, 2010.

    [Bow10d] Lewis Phylip Bowen. A measure-conjugacy invariant for free group actions. Ann. of Math. (2), 171(2):1387-1400, 2010.

    [Bow11a] Lewis Bowen. Entropy for expansive algebraic actions of residually finite groups. Ergodic Theory Dynam. Systems, 31(3):703-718, 2011.

    [Bow11b] Lewis Bowen. Weak isomorphisms between Bernoulli shifts. Israel J. Math., 183:93-102, 2011.

    [Bow12a] Lewis Bowen. Every countably infinite group is almost Ornstein. In Dynamical systems and group actions, volume 567 of Contemp. Math., pages 67-78. Amer. Math. Soc., Providence, RI, 2012.

    [Bow12b] Lewis Bowen. Sofic entropy and amenable groups. Ergodic Theory Dynam. Systems, 32(2):427-466, 2012.

    [Bow17a] Lewis Bowen. Examples in the entropy theory of countable group actions. submitted, 2017.

    [Bow17b] Lewis Bowen. Finitary random interlacements and the gaboriau-lyons problem. submitted, 2017.

    [CHR14] Laura Ciobanu, Derek F. Holt, and Sarah Rees. Sofic groups: graph products and graphs of groups. Pacific J. Math., 271(1):53-64, 2014.

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