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- W2263811781 abstract "Motivated by our previous results, we investigate structural properties of probability measure-preserving actions of sofic groups relative to their Pinsker factor. We also consider the same properties relative to the Outer Pinsker factor, which is another generalization of the Pinsker factor in the nonamenable case. The Outer Pinsker factor is motivated by extension for extensions, which fixes some of the pathological behavior of sofic entropy: namely increase of under factor maps. We show that an arbitrary probability measure-preserving action of a sofic group is mixing relative to its Pinsker and Outer Pinsker factors and, if the group is nonamenable, it has spectral gap relative to its Pinsker and Outer Pinsker factors. Our methods are similar to those we developed in Polish models and sofic entropy and based on representation-theoretic techniques. One crucial difference is that instead of considering unitary representations of a group we must consider *-representations of algebraic crossed products." @default.
- W2263811781 created "2016-06-24" @default.
- W2263811781 creator A5091290197 @default.
- W2263811781 date "2015-09-25" @default.
- W2263811781 modified "2023-09-27" @default.
- W2263811781 title "Mixing and Spectral Gap Relative to Pinsker Factors for Sofic Groups" @default.
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