Mixing Sets for Rigid Transformations

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.