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Title: A topological dynamical system with two different positive sofic entropies
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.  more » « less
Award ID(s):
1900386
PAR ID:
10319563
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Transactions of the American Mathematical Society, Series B
Volume:
9
Issue:
2
ISSN:
2330-0000
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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