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arXiv · 2006.08567

Ergodic cocycles of IDPFT systems and nonsingular Gaussian actions

Alexandre I. Danilenko·Mariusz Lemańczyk
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Abstract

It is proved that each Gaussian cocycle over a mildly mixing Gaussian transformation is either a Gaussian coboundary or sharply weak mixing. The class of nonsingular infinite direct products $T$ of transformations $T_n$, $n\in\Bbb N$, of finite type (IDPFT) is studied. It is shown that if $T_n$ is mildly mixing, $n\in\Bbb N$, the sequence of the Radon-Nikodym derivatives of $T_n$ is asymptotically translation quasi-invariant and $T$ is conservative then the Maharam extension of $T$ is sharply weak mixing. This techniques provides a new approach to the nonsingular Gaussian transformations studied recently by Arano, Isono and Marrakchi.

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Alexandre I. Danilenko, Mariusz Lemańczyk. 2020-06-15. Ergodic cocycles of IDPFT systems and nonsingular Gaussian actions. https://arxiv.org/abs/2006.08567

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