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arXiv · 2507.21620

Some Generic Properties of Processes

Benjamin Weiss
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Abstract

For a given ergodic measure preserving transformation T of a standard measure space each finite labelled partition defines an ergodic stationary process. There is a complete metric on the space of partitions which is separable. Various generic properties of these processes will be given. For example: 1. The generic partition defines a process that is not Rosenblatt mixing. 2. If T is a K-automorphism that is not Bernoulli then the generic partition is also K but not Bernoulli. Extensions to the relative setting and to actions of amenable groups will also be discussed.

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Benjamin Weiss. 2025-07-29. Some Generic Properties of Processes. https://arxiv.org/abs/2507.21620

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