Geodesic
Mixing Sets for Rigid Transformations
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 576-583

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It is shown that, for any infinite set $M\subset\mathbb N$ of density zero, there exists a rigid measure-preserving transformation of a probability space which is mixing along $M$. As examples, Gaussian actions and Poisson suspensions over infinite rank-one constructions are considered. Analogues of the obtained result for group actions and a method not using Gaussian and Poisson suspensions are also discussed.
Keywords: measure-preserving transformation, mild mixing, rigidity, mixing along a set, rank-one action
Mots-clés : Gaussian action, Poisson suspension. 
@article{MZM_2021_110_4_a7,
     author = {V. V. Ryzhikov},
     title = {Mixing {Sets} for {Rigid} {Transformations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {576--583},
     publisher = {mathdoc},
     volume = {110},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a7/}
}
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V. V. Ryzhikov. Mixing Sets for Rigid Transformations. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 576-583. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a7/