Geodesic
Joinings, intertwining operators, factors, and mixing properties of dynamical systems
Izvestiya. Mathematics , Tome 42 (1994) no. 1, pp. 91-114.

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This paper is mostly devoted to the following problem. If the Markov (stochastic) centralizer of a measure-preserving action $\Psi$ is known, what can be said about the Markov centralizer of the action $\Psi\otimes\Psi$? For a mixing flow with minimal Markov centralizer the author proves the triviality of the Markov centralizer of a Cartesian power of it, from which it follows that this flow possesses mixing of arbitrary multiplicity. For actions of the groups $\mathbf Z^n$ the analogous assertion holds if their tensor product with themselves does not possess three pairwise independent factors. In particular, this is true for actions of $\mathbf Z^n$ admitting a partial approximation and possessing mixing of multiplicity 2. 
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V. V. Ryzhikov. Joinings, intertwining operators, factors, and mixing properties of dynamical systems. Izvestiya. Mathematics , Tome 42 (1994) no. 1, pp. 91-114. http://geodesic.mathdoc.fr/item/IM2_1994_42_1_a4/

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