
Some results relating Kolmogorov complexity and entropy of amenable group actions
It was proved by Brudno that entropy and Kolmgorov complexity for dynami...
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Group theory, group actions, evolutionary algorithms, and global optimization
In this paper we use group, action and orbit to understand how evolution...
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Limit groups and groups acting freely on ^ntrees
We give a simple proof of the finite presentation of Sela's limit groups...
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The Group Theoretic Roots of Information I: permutations, symmetry, and entropy
We propose a new interpretation of measures of information and disorder ...
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On checkable codes in group algebras
We classify, in terms of the structure of the finite group G, all group ...
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Probabilistic constructions in continuous combinatorics and a bridge to distributed algorithms
The probabilistic method is a technique for proving combinatorial existe...
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Solving for best linear approximates
Our goal is to finally settle a persistent problem in Diophantine Approx...
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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 lefttranslations. 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 2colorings of random hypergraphs.
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