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arXiv · 2303.09546

Quasi-similarity, entropy and disjointness of ergodic systems

Valery V. Ryzhikov·Jean-Paul Thouvenot
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Abstract

Answering Vershik's question we show that quasi-similarity does not conserve the entropy, proving quasi-similarity of all Bernoulli actions of a countable infinite group. We prove also the following generalization of Pinsker's theorem: the actions with zero Kirillov-Kushnirenko $P$-entropy and the actions with completely positive $P$-entropy are disjoint. Poisson suspensions are used as examples.

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Valery V. Ryzhikov, Jean-Paul Thouvenot. 2023-03-16. Quasi-similarity, entropy and disjointness of ergodic systems. https://arxiv.org/abs/2303.09546

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