Uniform mixing and completely positive sofic entropy

Abstract

Let G be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving G-actions and show that it implies completely positive sofic entropy. When G contains an element of infinite order, we use this to produce an uncountable family of pairwise nonisomorphic G-actions with completely positive sofic entropy. None of our examples is a factor of a Bernoulli shift.

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