A topological dynamical system with two different positive sofic entropies
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- by Dylan Airey, Lewis Bowen and Yuqing Frank Lin HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 9 (2022), 35-98
Abstract:
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic entropy theory is a generalization of classical entropy theory in dynamics to actions by sofic groups. However, the sofic entropy of an action may depend on a choice of sofic approximation. All previously known examples showing this dependence rely on degenerate behavior. This paper exhibits an explicit example of a mixing subshift of finite type with two different positive sofic entropies. The example is inspired by statistical physics literature on 2-colorings of random hyper-graphs.References
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Additional Information
- Dylan Airey
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas
- Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey
- MR Author ID: 1106099
- Lewis Bowen
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas
- MR Author ID: 671629
- Yuqing Frank Lin
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas
- Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas
- MR Author ID: 1437606
- Received by editor(s): November 25, 2019
- Received by editor(s) in revised form: March 22, 2021, June 11, 2021, August 16, 2021, and October 9, 2021
- Published electronically: February 17, 2022
- Additional Notes: The first author was supported in part by NSF grant DGE-1656466. The second author was supported in part by NSF grant DMS-1900386. The third author was supported in part by NSF grant DMS-1900386
- © Copyright 2022 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 9 (2022), 35-98
- MSC (2020): Primary 37A35
- DOI: https://doi.org/10.1090/btran/101
- MathSciNet review: 4383230