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Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups

Published online by Cambridge University Press:  07 September 2017

BEN HAYES
BEN HAYES*
Affiliation:
Stevenson Center, Nashville, TN 37240, USA email benjamin.r.hayes@vanderbilt.edu
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Abstract

Let $G$ be a sofic group and $X$ a compact group with $G\curvearrowright X$ by automorphisms. Using (and reformulating) the notion of local and doubly empirical convergence developed by Austin, we show that in many cases the topological and the measure-theoretic entropy with respect to the Haar measure of $G\curvearrowright X$ agree. Our method of proof recovers all known examples. Moreover, the proofs are direct and do not go through explicitly computing the measure-theoretic or topological entropy.

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Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 4 , April 2019 , pp. 930 - 953
Copyright
© Cambridge University Press, 2017 

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