Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Weiss, Benjamin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891913322
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